Question

A solution method is shown.



What property is used in each step? Drag the appropriate property next to each step.

Response area with 6 blank spaces
Steps Property or Explanation
5 left-parenthesis x minus 3 right-parenthesis equals 20 Given
5 left-parenthesis x minus 3 right-parenthesis equals 20

one-fifth left-parenthesis 5 left-parenthesis x minus 3 right-parenthesis right parenthesis equals one-fifth left-parenthesis 20 right-parenthesis

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one-fifth left-parenthesis 5 left-parenthesis x minus 3 right-parenthesis right parenthesis equals one-fifth left-parenthesis 20 right-parenthesis

1 left-parenthesis x minus 3 right-parenthesis equals 4

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1 left-parenthesis x minus 3 right-parenthesis equals 4

x minus 3 equals 4

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x minus 3 equals 4

x minus 3 plus 3 equals 4 plus 3

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x minus 3 plus 3 equals 4 plus 3

x plus 0 equals 7

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x plus 0 equ

Answer 1

5(x − 3) = 20 — Given

(1/5)(5(x − 3)) = (1/5)(20) — Multiplication Property of Equality (multiply both sides by 1/5)

(1/5·5)(x − 3) = 4 ⇒ 1(x − 3) = 4 — Multiplicative Inverse Property (1/5·5 = 1), simplification

1(x − 3) = 4 ⇒ x − 3 = 4 — Multiplicative Identity Property (1·a = a)

x − 3 = 4 ⇒ x − 3 + 3 = 4 + 3 — Addition Property of Equality (add 3 to both sides)

x − 3 + 3 = 4 + 3 ⇒ x + 0 = 7 — Additive Inverse Property (−3 + 3 = 0), simplification

x + 0 = 7 ⇒ x = 7 — Additive Identity Property (x + 0 = x)