Question

Solve the inequality 7-7x > 35. ​(a) Write the solution in​ set-builder notation. ​(b) Write the solution in interval notation. ​(c) Graph the solution set.

Answer 1

a) {
`x:x\:<\:-4`}

b) The interval notation is
`(-\infty,-4)`

c) See graph in attachment

Explanation:

a) We want to solve the inequality

`7-7x\:>\:35`

We group like terms to obtain

`7-35\:>\:7x`

`\Rightarrow -28\:>\:7x`

Divide both sides by 7 ;

`\Rightarrow -4\:>\:x`

or

{
`x:x\:<\:-4`}

b) The interval notation is
`(-\infty,-4)`

c) Since the -4 is not part of the solution we use a hollow circle.

See attachment for the graphed solution