Question

How do you solve the inequality `7x – 2<3(3x + 2)`?

Answer 1

`x > 4`

Explanation:

`7x - 2 < 3(3x+2)`

First, use the distributive property to simplify `color(blue)(3(3x+2))`:

`color(blue)(3(3x+2) = (3 * 3x) + (3 * 2) = 9x + 6)`

Now put that back into the inequality:
`7x - 2 < 9x + 6`

Subtract `color(blue)6` from both sides of the inequality:
`7x - 2 quadcolor(blue)(-quad6) < 9x + 6 quadcolor(blue)(-quad6)`

`7x - 8 < 9x`

Subtract `color(blue)(7x)` from both sides of the inequality:
`7x - 8 quadcolor(blue)(-quad7x) < 9x quadcolor(blue)(-quad7x)`

`-8 < 2x`

Divide both sides by `color(blue)2`:
`-8/color(blue)(2) < (2x)/color(blue)2`

`4 < x`

This can be read as "4 is less than x".

Since we want the variable on the left side, it becomes "x is more than 4, or:

`x > 4`

Hope this helps!