Question

solve the following absolute value equation.

\\4|x - 8| = 36\\

\\x = ?, \quad \\

enter the smallest solution first.

Explanation:

Isolate the absolute value expression

Using the One-Step Equations knowledge point

$$
LATEXBLOCK0
$$

Set up the two case equations

To solve an absolute value equation of the form \(|u| = c\) (where \(c \ge 0\)), we split it into two separate linear equations:

$$ x - 8 = 9 \quad \text{or} \quad x - 8 = -9 $$

Solve the first case equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Solve the second case equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK2
$$

Order the solutions

Comparing the two solutions:

$$ -1 < 17 $$

The smallest solution is \(-1\) and the largest solution is \(17\).

Answer:

Solve the following absolute value equation.

$$4|x - 8| = 36$$

\(x =\) <blank>-1</blank>, <blank>17</blank>

Enter the smallest solution first.