Are you absolutely positive?

Algebra Level 2

For which values of $x$ is the following equation true?

$|3x + 5 | \geq |5x-1|$

Notation : $| \cdot |$ denotes the absolute value function .

-0.5 \geq x \geq 3

3 \geq x \geq -0.5

3 \leq x \leq -0.5

-0.5 \leq x \leq 3

2 solutions

Layla Reaves Staff
Jul 27, 2016

Roger Erisman
Aug 19, 2016

For absolute value statements such as absval(a) = absval(b) you must consider a = b and a = - b

3x + 5 = 5x - 1   Solving yields x = 3

or 3x + 5 = - 5x + 1 Solving yields x = - 1/2

This divides the graph into three zones. Choose an x value in each. Try x = - 1 , 0 , 4 in the original inequality.

x = - 1 yields 2 >= 6 not true

x = 0 yields 5 >= 1 TRUE

x = 4 yields 17 >= 19 not true

Solution is - 0..5 <= x <= 3 or in set notation [ -0.5 , 3]