5) Consider the sequence of steps to solve the equation: 2 (x - 4) + 5x = 9x - 10 Given ⇒ 2 (x - 4) + 6x = 9x - 10 Step 1 ⇒ 2x - 8 + 6x = 9x - 10 Step 2 ⇒ 2x + 6x - 8 = 9x - 10 Step 3 ⇒ 8x - 8 = 9x - 10 Step 4 ⇒ 8x - 8x - 8 = 9x - 8x - 10 Step 5 ⇒ 0 - 8 = x - 10 Step 6 ⇒ - 8 = x - 10 Step 7 ⇒ - 8 + 10 = x - 10 + 10 Step 8 ⇒ 2 = x + 0 Step 9 ⇒ 2 = x Which step in solving this equation is justified by the Addition Property of Equality?

Question

Charles Bonilla

Mathematics

30 January, 18:41

5) Consider the sequence of steps to solve the equation: 2 (x - 4) + 5x = 9x - 10 Given ⇒ 2 (x - 4) + 6x = 9x - 10 Step 1 ⇒ 2x - 8 + 6x = 9x - 10 Step 2 ⇒ 2x + 6x - 8 = 9x - 10 Step 3 ⇒ 8x - 8 = 9x - 10 Step 4 ⇒ 8x - 8x - 8 = 9x - 8x - 10 Step 5 ⇒ 0 - 8 = x - 10 Step 6 ⇒ - 8 = x - 10 Step 7 ⇒ - 8 + 10 = x - 10 + 10 Step 8 ⇒ 2 = x + 0 Step 9 ⇒ 2 = x Which step in solving this equation is justified by the Addition Property of Equality?

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Answers (1)

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Aidyn Vargas · Answer 1

The answer to this question is Step 7.

Step 7 ⇒ - 8 + 10 = x - 10 + 10

This is where 10 is being added to both sides. It is not Step 4 as that uses the Subtraction Property of Equality (which can be proved true by taking the addition of a negative number).