Question

1. $|4x + 5| = 26 - 3x$

show your work below your answer.
answer: { }

Explanation:

Step1: Consider two cases for the absolute value

Case 1: \(4x + 5 = 26 - 3x\) (when \(4x + 5\geq0\))

Step2: Solve Case 1 equation

\(4x + 3x = 26 - 5\)
\(7x = 21\)
\(x = 3\)
Check if \(4(3)+5 = 17\geq0\), which is true.

Case 2: \(4x + 5 = -(26 - 3x)\) (when \(4x + 5<0\))

Step3: Solve Case 2 equation

\(4x + 5 = -26 + 3x\)
\(4x - 3x = -26 - 5\)
\(x = -31\)
Check if \(4(-31)+5 = -119<0\), which is true.

Answer:

\(\{3, -31\}\)