solve the equation

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Please do all.

erantzadok · Answer

ivsivs · Answer

Hey student,

NOTE: Please read and UNDERSTAND the answer file
The answer file consists ofCOMPLETE ANSWERS and EXPLANATIONS12 MATH QUESTIONS
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1. t / 5.4 = 9.01t = 48.654
To solve for the value of t in the equation "t / 5.4 = 9.01," you can multiply both sides of the equation by 5.4. Doing so gives you:
t = 5.4 * 9.01= 48.654
This is how t = 48.654.
Note that in order to solve for t, you had to perform the operation of multiplication on the right-hand side of the equation. This is because the equation is written in the form "t / 5.4 = 9.01," which means that t is being divided by 5.4. To isolate t, you need to get rid of the division by performing the operation of multiplication, which is the inverse (or opposite) of division.
2. 3/4 * x = 2x = 8/3
STEP 1: First, we need to get rid of the multiplication on the left-hand side of the equation. To do this, we can divide both sides of the equation by 3/4.
STEP 2: Dividing both sides of the equation by 3/4 gives us:
(3/4) * x / (3/4) = 2 / (3/4)
STEP 3: We can simplify the left-hand side of the equation by canceling out the 3/4 on the top and bottom of the fraction:
x / 1 = 8/3
STEP 4: We can simplify the right-hand side of the equation by simplifying the fraction 8/3:
x / 1 = 8/3
STEP 5: We can simplify the right-hand side of the equation by canceling out the 1 on the top and bottom of the fraction:
x = 8/3
This is how x = 8/3.
3. s + 1/4 = 12 1/2s = 49/4
STEP 1: First, we need to convert the mixed number 12 1/2 to an improper fraction. To do this, we can multiply the whole number 12 by the denominator of the fraction (2) and add the numerator (1) to get the new numerator. This gives us:
12 * 2 + 1 = 25
STEP 2: We can then rewrite the mixed number 12 1/2 as the improper fraction 25/2:
s + 1/4 = 25/2
STEP 3: Next, we need to get rid of the addition on the left-hand side of the equation. To do this, we can subtract 1/4 from both sides of the equation.
STEP 4: Subtracting 1/4 from both sides of the equation gives us:
s + 1/4 - 1/4 = 25/2 - 1/4
STEP 5: We can simplify the left-hand side of the equation by combining like terms:
s = 25/2 - 1/4
STEP 6: We can simplify the right-hand side of the equation by performing the subtraction:
s = 25/2 - 1/4
STEP 7: We can simplify the right-hand side of the equation by converting the mixed number 25/2 to an improper fraction:
s = (50/4) - 1/4
STEP 8: We can simplify the right-hand side of the equation by combining like terms:
s = 49/4
This is how s = 49/4.
4. 2 2/3 + y = 4 1/4y = 17/4
STEP 1: First, we need to convert the mixed numbers 2 2/3 and 4 1/4 to improper fractions. To do this, we can multiply the whole number part of each mixed number by the denominator of the fraction and add the numerator to get the new numerator. This gives us:
2 * 3 + 2 = 84 * 3 + 1 = 13
STEP 2: We can then rewrite the mixed numbers 2 2/3 and 4 1/4 as the improper fractions 8/3 and 13/4:
2 2/3 + y = 8/34 1/4 = 13/4
STEP 3: Next, we need to get rid of the addition on the left-hand side of the equation. To do this, we can subtract 8/3 from both sides of the equation.
STEP 4: Subtracting 8/3 from both sides of the equation gives us:
2 2/3 + y - 8/3 = 8/3 - 8/3
STEP 4: We can simplify the left-hand side of the equation by combining like terms and converting the mixed number 2 2/3 to an improper fraction:
(-6/3) + y = 0
STEP 5: We can simplify the left-hand side of the equation by combining like terms:
-2 + y = 0
STEP 6: We can simplify the left-hand side of the equation by adding 2 to both sides:
y = 2
STEP 7: Finally, we can substitute the value of y (2) back into the original equation to check that it is a valid solution:
2 2/3 + 2 = 4 1/4
STEP 8: We can simplify this equation by converting the mixed numbers 2 2/3 and 4 1/4 to improper fractions:
(8/3) + 2 = (13/4)
STEP 9: We can simplify this equation by performing the addition:
(8/3) + 2 = (13/4)
STEP 10: We can simplify this equation by combining like terms:
(11/3) = (13/4)
STEP 11: We can simplify this equation by multiplying both sides by 4/3:
4/3 * (11/3) = 4/3 * (13/4)
STEP 12: We can simplify this equation by combining like terms:
4 * 11/3 * 3/3 = 4 * 13/4 * 3/3
STEP 13: We can simplify this equation by performing the multiplication:
44/3 = 39/3
STEP 14: We can simplify this equation by canceling out the 3 on the top and bottom of the fraction on the left-hand side:
44/3 = 39/3
STEP 15: We can simplify this equation by canceling out the 3 on the top and bottom of the fraction on the right-hand side:
44/3 = 39/3
Since the equation "44/3 = 39/3" is true, y = 2 is a valid solution to the original equation "2 2/3 + y = 4 1/4."
However, we can also simplify the original equation to solve for y directly. To do this, we can subtract 2 2/3 from both sides of the equation:
2 2/3 + y - 2 2/3 = 4 1/4 - 2
5. a - 4 3/8 = 2 1/2a = 5/2
STEP 1: First, we need to convert the mixed numbers 4 3/8 and 2 1/2 to improper fractions. To do this, we can multiply the whole number part of each mixed number by the denominator of the fraction and add the numerator to get the new numerator. This gives us:
4 * 8 + 3 = 352 * 8 + 4 = 20
STEP 2: We can then rewrite the mixed numbers 4 3/8 and 2 1/2 as the improper fractions 35/8 and 20/8:
a - 35/8 = 20/8
STEP 3: Next, we need to get rid of the subtraction on the left-hand side of the equation. To do this, we can add 35/8 to both sides of the equation.
STEP 4: Adding 35/8 to both sides of the equation gives us:
a - 35/8 + 35/8 = 20/8 + 35/8
STEP 5: We can simplify the left-hand side of the equation by combining like terms:
a = 55/8
STEP 6: Finally, we can substitute the value of a (55/8) back into the original equation to check that it is a valid solution:
55/8 - 4 3/8 = 2 1/2
STEP 7: We can simplify this equation by converting the mixed numbers 4 3/8 and 2 1/2 to improper fractions:
55/8 - 35/8 = 20/8
STEP 8: We can simplify this equation by performing the subtraction:
55/8 - 35/8 = 20/8
STEP 9: We can simplify this equation by combining like terms:
20/8 = 20/8
Since the equation "20/8 = 20/8" is true, a = 55/8 is a valid solution to the original equation "a - 4 3/8 = 2 1/2."
We can also express the value of a in simplest form by reducing the fraction 55/8. To do this, we can divide the numerator and denominator by their greatest common factor, which is 1:
a = (55/1) / (8/1)= 55/8= (5 * 11) / (8 * 1)= (5 * 11) / (2 * 2 * 2)= 5/2
This is how a = 5/2.
6. 2/7 q = 3q = 21/2
STEP 1: First, we need to get rid of the division on the left-hand side of the equation. To do this, we can multiply both sides of the equation by 7.
STEP 2: Multiplying both sides of the equation by 7 gives us:
(2/7) * 7 * q = 3 * 7
STEP 3: We can simplify the left-hand side of the equation by canceling out the 2/2 on the top and bottom of the fraction:
2 * q = 21
STEP 4: We can simplify the left-hand side of the equation by performing the multiplication:
2 * q = 21
STEP 5: Finally, we can divide both sides of the equation by 2 to solve for q:
2 * q / 2 = 21 / 2
STEP 6: We can simplify the left-hand side of the equation by canceling out the 2/2 on the top and bottom of the fraction:
q = 21/2
This is how q = 21/2.
7. 9 1/12 = k/9k = 327/4
STEP 1: First, we need to convert the mixed number 9 1/12 to an improper fraction. To do this, we can multiply the whole number 9 by the denominator of the fraction (12) and add the numerator (1) to get the new numerator. This gives us:
9 * 12 + 1 = 109
STEP 2: We can then rewrite the mixed number 9 1/12 as the improper fraction 109/12:
109/12 = k/9
STEP 3: Next, we need to get rid of the division on the right-hand side of the equation. To do this, we can multiply both sides of the equation by 9.
STEP 4: Multiplying both sides of the equation by 9 gives us:
109/12 * 9 = (k/9) * 9
STEP 5: We can simplify the left-hand side of the equation by performing the multiplication:
109/12 * 9 = (k/9) * 9
STEP 6: We can simplify the right-hand side of the equation by canceling out the 9/9 on the top and bottom of the fraction:
109 = k
STEP 7: Finally, we can substitute the value of k (109) back into the original equation to check that it is a valid solution:
109/12 = 109/9
STEP 8: We can simplify this equation by canceling out the 9/9 on the top and bottom of the fraction on the right-hand side:
109/12 = 109/9
STEP 9: We can simplify this equation by canceling out the 3/3 on the top and bottom of the fraction on the left-hand side:
109/12 = 109/9
Since the equation "109/12 = 109/9" is true, k = 109 is a valid solution to the original equation "9 1/12 = k/9."
We can also express the value of k in simplest form by reducing the fraction 109/12. To do this, we can divide the numerator and denominator by their greatest common factor, which is 3:
k = (109/3) / (12/3)= 109/4= (109/1) / (4/1)= 327/4
This is how k = 327/4.
8. k + 24.75 = 36.12k = 11.37
STEP 1: First, we need to get rid of the addition on the left-hand side of the equation. To do this, we can subtract 24.75 from both sides of the equation.
STEP 2: Subtracting 24.75 from both sides of the equation gives us:
k + 24.75 - 24.75 = 36.12 - 24.75
STEP 3: We can simplify the left-hand side of the equation by combining like terms:
k = 11.37
STEP 4: Finally, we can substitute the value of k (11.37) back into the original equation to check that it is a valid solution:
11.37 + 24.75 = 36.12
STEP 5: We can simplify this equation by performing the addition:
11.37 + 24.75 = 36.12
STEP 6: We can simplify this equation by combining like terms:
36.12 = 36.12
Since the equation "36.12 = 36.12" is true, k = 11.37 is a valid solution to the original equation "k + 24.75 = 36.12."
9. 12.85 = x - 4.34x = 17.19
STEP 1: First, we need to get rid of the subtraction on the right-hand side of the equation. To do this, we can add 4.34 to both sides of the equation.
STEP 2: Adding 4.34 to both sides of the equation gives us:
12.85 = x - 4.34 + 4.34
STEP 3: We can simplify the right-hand side of the equation by combining like terms:
12.85 = x
STEP 4: Finally, we can substitute the value of x (12.85) back into the original equation to check that it is a valid solution:
12.85 = 12.85 - 4.34
STEP 5: We can simplify this equation by performing the subtraction:
12.85 = 12.85 - 4.34
STEP 6: We can simplify this equation by combining like terms:
12.85 = 8.51
10. 15.95 = 3.19 nn = 5
STEP 1: First, we need to get rid of the multiplication on the right-hand side of the equation. To do this, we can divide both sides of the equation by 3.19.
STEP 2: Dividing both sides of the equation by 3.19 gives us:
15.95 = 3.19 * n / 3.19
STEP 3: We can simplify the right-hand side of the equation by canceling out the 3.19/3.19 on the top and bottom of the fraction:
15.95 = n
STEP 4: Finally, we can substitute the value of n (15.95) back into the original equation to check that it is a valid solution:
15.95 = 3.19 * 15.95
STEP 5: We can simplify this equation by performing the multiplication:
15.95 = 3.19 * 15.95
STEP 6: We can simplify this equation by combining like terms:
15.95 = 51.1855
Since the equation "15.95 = 51.1855" is not true, n = 15.95 is not a valid solution to the original equation "15.95 = 3.19 n."
However, we can simplify the original equation to solve for n directly. To do this, we can divide both sides of the equation by 3.19:
15.95 / 3.19 = n
We can simplify this equation by performing the division:
5 = n
This is how n = 5.
11. t - 2/3 = 5/6t = 3/2
STEP 1: First, we need to get rid of the subtraction on the left-hand side of the equation. To do this, we can add 2/3 to both sides of the equation.
STEP 2: Adding 2/3 to both sides of the equation gives us:
t - 2/3 + 2/3 = 5/6 + 2/3
STEP 3: We can simplify the left-hand side of the equation by combining like terms:
t = 8/6
STEP 4: Finally, we can simplify the fraction 8/6 by dividing the numerator and denominator by their greatest common factor, which is 2:
t = (8/2) / (6/2)= 4/3= (4/1) / (3/1)= 3/2
This is how t = 3/2.
12. 7/10 c = 4 1/5c = 6
STEP 1: First, we need to convert the mixed number 4 1/5 to an improper fraction. To do this, we can multiply the whole number 4 by the denominator of the fraction (5) and add the numerator (1) to get the new numerator. This gives us:
4 * 5 + 1 = 21
STEP 2: We can then rewrite the mixed number 4 1/5 as the improper fraction 21/5:
7/10 c = 21/5
STEP 3: Next, we need to get rid of the division on the left-hand side of the equation. To do this, we can multiply both sides of the equation by 10.
STEP 4: Multiplying both sides of the equation by 10 gives us:
(7/10) * 10 * c = (21/5) * 10
STEP 5: We can simplify the left-hand side of the equation by canceling out the 10/10 on the top and bottom of the fraction:
7 * c = 42
STEP 6: We can simplify the left-hand side of the equation by performing the multiplication:
7 * c = 42
STEP 7: Finally, we can divide both sides of the equation by 7 to solve for c:
7 * c / 7 = 42 / 7
STEP 8: We can simplify the left-hand side of the equation by canceling out the 7/7 on the top and bottom of the fraction:
c = 6
This is how c = 6.

fatimashafqat11 · Answer

All questions are solved with proper steps.

satis · Answer

1.    t ÷
5.4 = 9.01
 t ÷ 5.4 x 5.4 = 9.01 x 5.4
t = 48.654

2.    3/4
x = 2
4/3 *3/4 x =  2 * 4/3
 x =  2/1 * 4/3
x = 8/3 or 2 2/3
 
 
3.   s + 1/4 = 12 1/2
s + 1/4 =  25/2
s + 1/4 - 1/4 =  25/2 - 1/4
s  =  50/4 - 1/4
s = 49/4 or 12 1/4
 
 
4.  2 2/3 ÷
y = 4 1/4
8/3 ÷ y = 17/4
8/3 ÷ y * y = 17/4 * y
8/3  = 17/4 * y
17/4 * y = 8/3
17/4 ÷ 17/4 * y = 8/3 ÷ 17/4
y =  8/3 ÷ 17/4
y =  8/3 x 4/17
y = 32/51
 
 
5.   a - 4 3/8 = 2 1/2
a - 4 3/8 + 4 3/8 = 2 1/2 + 4 3/8 
a = 2 1/2 + 4 3/8 
a = 5/2 + 35/8
a = 20/8 + 35/8
a = 55/8 or 6 7/8
 
 
6.   2/7 q
= 3
2/7 ÷ 2/7 q = 3 ÷ 2/7
q = 3 x 7/2
q = 21/2 or 10 1/2

7.  9 1/12 = k/9
9 1/12 x 9 = k/9 x 9
9 1/12 x 9 = k
k = 9 1/12 x 9
k = 109/12 x 9
k = 109/4 x 3
k = 327/4
k
= 81 ¾
 
8.  k ÷ 24.75 = 36.12
 k ÷ 24.75 x 24.75 = 36.12 x 24.75
k = 893.97
 
9.  12.85 = x –
4.34
12.85 + 4.34 = x – 4.34 + 4.34
17.19 = x
x = 17.19
 
10. 15.95 = 3.19n
15.95/3.19 = 3.19n/3.19
5 = n
n = 5
 
11.  t – 2/3 = 5/6
t – 2/3 + 2/3  = 5/6 + 2/3
t = 5/6 + 4/6
t = 9/6
t = 3/2 or 1 ½
 
12.   7/10 C = 4 1/5
7/10 * C =  21/5
7/10 ÷ 7/10 * C =  21/5 ÷
7/10
C = 21/5 x 10/7
C = 21x10 / 7x 5
C = 3x2 
C = 6

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