Home > Algebra > Compound Inequalities

How do you solve and graph the compound inequality #-1 < 2x + 5 < 13# ?

Answer 1

Kennedy Adams

You first try to get the #x# 'free'

Subtract #5# everywhere: #-6<2x<8#

Now divide everything by #2# #-3 < x<4#

In the graph every #y#-value between -1 and 13 is valid: graph{2x+5 [-24.9, 26.47, -4.01, 21.63]}

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

Answer 2

Jameson Allen

To solve the compound inequality -1 < 2x + 5 < 13, first subtract 5 from all parts to isolate 2x: -1 - 5 < 2x < 13 - 5, which simplifies to -6 < 2x < 8. Then, divide all parts by 2 to solve for x: -3 < x < 4. To graph this on a number line, plot an open circle at -3 and 4, then shade between them to represent all values of x that satisfy the compound inequality.

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 the compound inequality #-1 &lt; 2x + 5 &lt; 13# ?

How do you solve and graph the compound inequality #-1 < 2x + 5 < 13# ?