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.

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.`**

The inequality 7x+12>9x-8 has to be solved.

7x+12>9x-8

An inequality is not affected if both the sides are multiplied by a positive number or if a positive number is added or subtracted from both the sides.

7x+12>9x-8

Add -9x+8 to both the sides

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

-2x + 20 > 0

Add 2x to both the sides

20 > 2x

Divide both the sides by 2

10>x

The solution of the inequality is `(-oo, 10)`

7x+12>9x-8

treat the > or< or>= or<= signs as an = sign when doing these problems except *when you divide by a negitive number, flip the sign!*

i.e.

-3X>9

X<-3

for this problem

7x+12>9x-8

subtract 7x from both sides and add 8 to both sides

20>2X

divide by 2

X<10, or 10>X

solve 7x+12>9x-8

12>2x-8 subtract 7x from both sides

20>2x add 8 to both sides

10>x divide both sides by 8

`7x+12gt9x-8` get the like terms on the same side

`12+8 gt 9x-7x`

`20 gt 2x`

divide by 2

`(20)/2 gt (2x)/2`

`10gtx`

Solve

`7x+12>9x-8`

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

`7x+20-7x>9x-7x`

`20>2x`

`(20)/2>(2x)/2`

`10>x`

`or`

`x<10`