Question

Eduardo solved the following inequality, and his work is shown below: −5(x + 4) + 21 ≥ −3 + 4(x − 8) −5x − 20 + 21 ≥ −3 + 4x − 32 −5x + 1 ≥ 4x − 35 −9x ≥ −36 x ≥ 4

Answer 1

GIVEN :

Eduardo solved the following inequality, and his work is given below :

-5(x+4)+21 ≥ -3+4(x-8)

-5x-20+21 ≥ -3+4x-32

-5x+1 ≥ 4x-35

-9x ≥ -36

x ≥ 4

TO FIND :

The mistake did Eduardo make in solving the inequality

SOLUTION :

Given that Eduardo solved the following inequality, and his work is shown below :

-5(x+4)+21 ≥ -3+4(x-8)

-5(x)+(-5)(4) + 21 ≥ -3+4(x)-4(8)

-5x-20+21 ≥ -3+4x-32

-5x+1 ≥ 4x-35

-5x-4x ≥ -35-1

-9x ≥ -36

x ≥ 4

Actually the corrected steps are,

9x ≤ 36

∴ x ≤ 4

When comparing Eduardo's work in the next step to -9x ≥ -36 is 9x ≤ 36 correct but he did not change the inequality ≥ to ≤  when dividing by -9

Option A) When dividing by −9, he did not change the ≥ to ≤. is correct.