How do you solve and graph #5x < 3 (x-4) + 7#?

1 Answer
Noah G
Feb 9, 2016

For linear inequalities, you solve for x just as you would in an equation except you flip the inequality sign's direction if multiplying or dividing by a negative number.

Explanation:

#5x < 3x - 12 + 7#

#5x - 3x < -12 + 7#

#2x < -5#

#x < -5/2#

Since this is a single variable inequality, you will graph it on a number line. See the following diagram. enter image source here

In the diagram, the black rectangle has been placed over the solution area (any numbers smaller than -2.5, for infinity).

Practice exercises:

  1. Solve the following inequalities, and graph them on the number lines:

a) #2x - 3(x + 4) > 5x#
enter image source here

b) #3(2x + 4) + 2(2x - 6) < 4/(2(x - 1))#

enter image source here

Good luck!

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