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Since `7x` and `-9x` are like terms, add `-9x` to` 7x` to get `-2x` .

`-2x+12gt-8`


Move all terms not containing x to the right-hand side of the inequality.

`12-2xgt-8 `


Move all terms not containing x to the right-hand side of the inequality.

`-2xgt-20 `


Divide each term in the inequality by `-2`

Remember that if you multiply or divide negative numbers, the inequality symbol reverses.

`xlt10`

This shows that the solution of the inequality is all real numbers less than 10.

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Solve `7x + 12 gt 9x - 8` .

In order to solve inequalities we must isolate the variable, just like in equations.

First, subtract 9x from each side.

`7x - 9x + 12 > 9x - 8 - 9x`

`-2x + 12 > -8`

Subtract 12 from each side.

`-2x + 12 - 12 > -8 - 12`

`-2x > -20`

Now, divide both sides by -2.  However, when you multiply or divide an inequality by a negative value the inequality reverses direction.

`(-2x)/(-2) < (-20)/(-2)`

`x < 10`

The solution is `x<10.`

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