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

Answer:

$-3 < x < -2$

Step-by-step 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: $-3 < x < -2$