7) x + 3 = (x - 5)2: x = 13
Let's start with this part of the equation:
(x - 5) x 2
Switch:
= 2(x - 5)
Apply the distributive law: a(b - c) = ab - ac
a = 2, b = x, c = 5
= 2x - 2 x 5
Multiply the numbers: 2 x 5 = 10
= 2x - 10
Plug in the expression:
x + 3 = 2x - 10
Subtract 3 from both sides
x + 3 - 3 = 2x - 10 - 3
Simplify
x = 2x - 13
Subtract 2x from both sides
x - 2x = 2x - 13 - 2x
Simplify
-x = -13
Divide both sides by -1
-x / -1 = -13 / -1
Simplify
x = 13
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8) x4 = x - 10: x = -10/3 or x = 3.33(repeating)
Let's rewrite this equation:
x * 4 = x - 10
Subtract x from both sides
x * 4 - x = x - 10 - x
Simplify
3x = -10
Divide both sides by 3
3x / 3 = -10 / 3
Simplify
x = -10/3 - as a fraction
x = 3.33(repeating) - as a decimal
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9) x3 = 5 – x : x = 5/4 or x = 1.25
Let's rewrite this equation:
x * 3 = 5 - x
Add x to both sides
x * 3 + x = 5 - x + x
Simplify
4x = 5
Divide both sides by 4
4x / 4 = 5 / 4
Simplify
x = 5/4 - as a fraction
x = 1.25 - as a decimal