Question

Carson solved an inequality using the steps shown.

Given: -2(n-3) - 5 >9
Step 1: -2n + 6 - 5> 9
Step 2: -2n + 1 > 9
Step 3: -2n > 8
Step 4: n >-4
Which step contains Carson's first mistake?

Answer 1

Carson's first mistake occurs in Step 1, where he incorrectly distributes the negative sign.

Step-by-step explanation:

Carson's first mistake occurs in Step 1, where he incorrectly distributes the negative sign in front of the parentheses. The correct distribution should be: -2(n-3) - 5 = -2n + 6 - 5.

Step 2, Step 3, and Step 4 are all correct. In Step 2, Carson combines like terms: -2n + 6 - 5 > 9 becomes -2n + 1 > 9. In Step 3, Carson isolates the variable by subtracting 1 from both sides: -2n + 1 > 9 becomes -2n > 8. Finally, in Step 4, Carson divides both sides by -2, remembering to reverse the inequality sign when dividing by a negative number: -2n > 8 becomes n > -4.

Answer 2

Step 4 contains his mistake . Because while changing the signs , one has to also reverse the inequality sign