Question

3. Sophie solved the inequality

as shown. Explain Sophie's error
and give the correct solution to
the inequality.
-5(x - 1) > -7x + 19
-5X - 5 >-7x +19
2x - 5 > 19
2x > 24
X>12

Answer 1

After she distribute the
`x` and
`-1` by
`-5`, the after you get
`-5x - 5 > -7x + 19`, she put a negative
`5` instead of a positive
`5`, and would be written as
`-5x + 5 > -7x + 19`.

Explanation:

Solve the inequality for the correct solution:

`-5(x - 1) > -7x + 19`

-Use Distributive Property:

`-5(x - 1) > -7x + 19`

`-5x + 5 > -7x + 19`

-Take
`7x` and add it to
`-5x`:

`-5x + 5 + 7x > -7x + 7x + 19`

`2x + 5 > 19`

-Subtract
`5` to both sides:

`2x + 5 - 5 > 19 - 5`

`2x > 14`

-Divide both sides by
`2`:

`(2x)/(2) > (14)/(2)`

`\boxed {x > 7}`