Home > Algebra > Compound Inequalities

How do you solve and graph #2x > -6# and #x - 4 < 3#?

Answer 1

Kennedy Adams

First reduce both inequalities:

(1) #2x> -6->x> -3# (divided both sides by 2) and (2) #x-4<3->x<7# (added 4 to both sides)

Summary: #-3 < x<7#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Adamson

To solve the inequality 2x > -6, you divide both sides by 2 to isolate x, giving you x > -3. To solve the inequality x - 4 < 3, you add 4 to both sides, giving you x < 7. So, the solution to the system of inequalities is -3 < x < 7. To graph this solution on a number line, you plot an open circle at -3 and another open circle at 7, then shade the region between them.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph #2x &gt; -6# and #x - 4 &lt; 3#?

How do you solve and graph #2x > -6# and #x - 4 < 3#?