Question

How do you solve the inequality `(x +4) + (x+6)> 3x - 1`?

Answer 1

`x<11`

Explanation:

1. Add like terms.

`(x+4)+(x+6)>3x-1`

`2x+10>3x-1`

2. Subtract 10 from both sides.

`2x+10` `color(red)(-10)>3x-1` `color(red)(-10)`

`2x>3x-11`

3. Subtract 3x from both sides.

`2x` `color(red)(-3x)>3x` `color(red)(-3x)-11`

`-x` `>` `-11`

4. Divide both sides by -1.

`-xcolor(red)(-:-1)` `>` `-11color(red)(-:-1)`

`x>11`

5. Flip the inequality sign.
Whenever you divide by a negative number, you must flip the inequality sign, even if you divide a negative number by another negative number.

`color(green)(x<11)`