Question

Solve the inequality 2(7x -2) > 9x + 6

Answer 1

`2\left(7x-2\right)>9x+6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(2,\:\infty \:\right)\end{bmatrix}`

Explanation:

`2\left(7x-2\right)>9x+6`

`2\left(7x-2\right)`

`$a=2,\:b=7x,\:c=2$`

`=2\cdot \:7x-2\cdot \:2`

`=14x-4`

`14x-4>9x+6`

`\mathrm{Add\:}4\mathrm{\:to\:both\:sides}`

`14x-4+4>9x+6+4`

`\mathrm{Simplify}`

`14x>9x+10`

`\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}`

`14x-9x>9x+10-9x`

`\mathrm{Simplify}`

`5x>10`

`\mathrm{Divide\:both\:sides\:by\:}5`

`(5x)/(5)>(10)/(5)`

`\mathrm{Simplify}`

`x>2`