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.

Question

asked Jul 11, 2020 191k views

1 Answer

Eduardomozart · Answer 1 · 2020-07-16T18:42:02+0000

Answer:

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