Question

Error analysis: Determine the mistakes in solving the following inequality and explain.

-5x - 3 > 11 - 2x
-7x - 3 > 11
-7x > 14
x > -2

Answer 1

The student made a mistake by incorrectly combining like terms in the inequality -5x - 3 > 11 - 2x. The correct solution is x < -2.43.

Step-by-step explanation:

The mistake in solving the inequality -5x - 3 > 11 - 2x is that the student incorrectly combined like terms. To solve this inequality, we need to isolate x on one side. Here are the correct steps:

1. Combine like terms on both sides of the inequality: -5x - 3 > 11 - 2x becomes -7x - 3 > 14.
2. Add 3 to both sides of the inequality to isolate the x term: -7x - 3 + 3 > 14 + 3 becomes -7x > 17.
3. Divide both sides of the inequality by -7, remembering to flip the direction of the inequality when dividing by a negative number: -7x/-7 < 17/-7 becomes x < -17/7 or x < -2.43 (rounded to two decimal places).

Therefore, the correct solution to the inequality is x < -2.43. The student made a mistake by incorrectly combining like terms, resulting in an incorrect solution of x > -2.