Question

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

31 < –5x + 6
25 < –5x
–5 < x

The student should have added 6 to both sides instead of subtracting it.

The student divided 25/–5 incorrectly.

The student should have switched the direction of the inequality sign to get –5> x for a final answer.

Answer 1

Answer: Last option.

Explanation:

Given the inequality:

`31 < -5x + 6`

The procedure to solve it is this:

- Subtract 6 from both sides:

`31 -6< -5x + 6-6\\\\25<-5x`

- Divide both sides by -5 (Since we are dividing both sides by a negative number , we must switch the direction of the inequality sign):

`(25)/(-5)<(-5x)/(-5)\\\\-5>x`

Therefore, the student’s error in solving the following inequality is: The student should have switched the direction of the inequality sign to get
`-5>x` for a final answer.

Answer 2

The correct option is:

The student should have switched the direction of the inequality sign to get –5> x for a final answer

Explanation:

The students has made a mistake in the 3rd step.

We know that when we multiply or divide any negative number on both sides of the inequality, the sign of inequality reverse its direction.

In step 3 the student divided 25 by -5 but did not switch direction of the inequality sign.

Therefore the correct option is: The student should have switched the direction of the inequality sign to get –5> x for a final answer....