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Solve the absolute value equation. Check your solutions.

|x+4|=10

Solve the absolute value equation. Check your solutions. $\newline$ $|x+4|=10$

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Integer inequalities with absolute values

Full solution

Q. Solve the absolute value equation. Check your solutions.

\newline

|x+4|=10

Understand absolute value equation: Step $1$ : Understand the absolute value equation. $\newline$ The equation $\lvert x+4 \rvert = 10$ means the expression inside the absolute value, $x+4$ , can be either $10$ or $-10$ .
Solve for x $(x+4=10)$ : Step $2$ : Solve for x when $x+4 = 10$ . $x + 4 = 10$ $x = 10 - 4$ $x = 6$
Solve for $x$ ( $x+4=-10$ ): Step $3$ : Solve for $x$ when $x+4 = -10$ . $x + 4 = -10$ $x = -10 - 4$ $x = -14$
Check solutions in original equation: Step $4$ : Check the solutions in the original equation. $\newline$ For $x = 6$ : $\newline$ $|x + 4| = |6 + 4| = |10| = 10$ , which is correct. $\newline$ For $x = -14$ : $\newline$ $|x + 4| = |-14 + 4| = |-10| = 10$ , which is also correct.

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