Let’s solve each problem one by one. The goal is to make
x the subject — that means we want to get x alone on one side of the equation.
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1) 4x - t = a
Add t to both sides:
4x = a + t
Divide both sides by 4:
x = (a + t)/4
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2) 9 - x/(y-2) = z
Subtract 9 from both sides:
- x/(y-2) = z - 9
Multiply both sides by -1:
x/(y-2) = 9 - z
Multiply both sides by (y - 2):
x = (9 - z)(y - 2)
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3) x/y + 5 = 7
Subtract 5 from both sides:
x/y = 2
Multiply both sides by y:
x = 2y
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4) (1/3)x + p = q
Subtract p from both sides:
(1/3)x = q - p
Multiply both sides by 3:
x = 3(q - p)
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5) bx/a = c
Multiply both sides by a:
bx = ac
Divide both sides by b:
x = ac/b
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6) -2Tx - cx = -10c
Factor out x on the left:
x(-2T - c) = -10c
Divide both sides by (-2T - c):
x = -10c / (-2T - c)
We can simplify signs: multiply numerator and denominator by -1:
x = 10c / (2T + c)
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7) 1 - 13m = 2h + x
Subtract 2h from both sides:
1 - 13m - 2h = x
So:
x = 1 - 13m - 2h
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8) 4x + 2 = 3k
Subtract 2 from both sides:
4x = 3k - 2
Divide by 4:
x = (3k - 2)/4
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9) -x - y - z = 8/7
Add y and z to both sides:
-x = 8/7 + y + z
Multiply both sides by -1:
x = -8/7 - y - z
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10) 5 - x = 21 + q
Subtract 5 from both sides:
-x = 16 + q
Multiply by -1:
x = -16 - q
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11) 5br - t - x = 0
Add x to both sides:
5br - t = x
So:
x = 5br - t
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12) -9x - g = -22g
Add g to both sides:
-9x = -21g
Divide by -9:
x = (-21g)/(-9) = 21g/9 = 7g/3
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Final Answer:
1) x = (a + t)/4
2) x = (9 - z)(y - 2)
3) x = 2y
4) x = 3(q - p)
5) x = ac/b
6) x = 10c / (2T + c)
7) x = 1 - 13m - 2h
8) x = (3k - 2)/4
9) x = -8/7 - y - z
10) x = -16 - q
11) x = 5br - t
12) x = 7g/3
Parent Tip: Review the logic above to help your child master the concept of manipulating formulas worksheet.
