Expert Answers
kingattaskus12 eNotes educator| Certified Educator

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


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.


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

baxthum8 eNotes educator| Certified Educator

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.`

tonys538 | Student

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


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.


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


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


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




for this problem


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


divide by 2

X<10, or 10>X

nisarg | Student

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

atyourservice | Student

`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`


aruv | Student










Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question