Question

Jill solved the inequality -x/4 < (x+2)/3

Her solution is shown:

Step 1 : -3x<4x+8
Step 2: -3x-4x <8
Step 3: -7x<8
Step 4: x< -8/7

Explain the mistake Jill made while solving for x.


I don't see anything wrong... is it a trick questions???

Answer 1

Jill did not change the symbol of inequality from minor (< ) to major (>) in the Step 4

Explanation:

we have

`-(x)/(4)  < (x+2)/(3)`

step 1

Multiply by 12 both sides

`(12)(-(x)/(4))  < (12)((x+2)/(3))`

`-3x < 4(x+2)`

`-3x < 4x+8`

step 2

Group terms

`-3x-4x < 8`

step 3

Combine like terms

`-7x < 8`

step 4

Divide by -7 both sides

`x > -8/7`

Remember that when you multiply an inequality by -1 the < symbol changes to the > symbol

so

Jill did not change the symbol of inequality from minor (< ) to major (>) in the Step 4