Question

Find the student’s error in solving the following inequality.

2 < –3x –4 < 5
6 < –3x < 5
–2 > x > –5/3

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

The student divided 6/–3 incorrectly.

The student should not have switched the direction of the sign in the final step.

Answer 1

`-3 < x < -2`

Explanation:

Seperate compound inequalities into system of inequalities:
`\left \{ {{-3x-4 > 2} \atop {-3x-4 > 5}} \right.`

Rearrange unknown terms to the left side of the equation:
`-3x > 2+4`

Calculate the sum or difference:
`-3x > 6`

Reduce the greatest common factor for both sides of the inequality:
`-x > 2`

Divide both sides of the inequality by the coefficient of the variable:
`x < -2`

Rearrange unknown terms to the left side of the equation:
`-3x < 5+4`

Calculate the sum or difference:
`-3x < 9`

Reduce the greatest common factor for both sides of the inequality:
`-x < 3`

Divide both sides of the inequality by the coefficient of the variable:
`x > -3`

Find the intersection:
`-3 < x < -2`

Answer:
`-3 < x < -2`

Answer 2

The student should have added 4 to all parts (left, middle, and right) to get 6 < –3x < 9.

Explanation: