Solve for all values of x in simplest form. |x+6|=9 Answer: x=

Understand absolute value equation: Understand the absolute value equation |x+6|=9. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |x+6|=9 means that the expression x+6 is 9 units away from zero on the number line. This can happen in two ways: either x+6 is 9 or x+6 is -9.Set up two equations: Set up two separate equations to solve for x. Since x+6 can be either 9 or -9, we write two equations: 1. x+6 = 9 2. x+6 = -9Solve first equation: Solve the first equation x+6 = 9. Subtract 6 from both sides of the equation to isolate x: x + 6 - 6 = 9 - 6 x = 3Solve second equation: Solve the second equation x+6 = -9. Subtract 6 from both sides of the equation to isolate x: x + 6 - 6 = -9 - 6 x = -15

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Solve for all values of
x in simplest form.

|x+6|=9
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $|x+6|=9$ $\newline$ Answer: $x=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

|x+6|=9

\newline

Answer:

x=

Understand absolute value equation: Understand the absolute value equation $|x+6|=9$ . $\newline$ The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|x+6|=9$ means that the expression $x+6$ is $9$ units away from zero on the number line. This can happen in two ways: either $x+6 = 9$ or $x+6 = -9$ .
Set up two equations: Set up two separate equations to solve for $x$ . Since $x+6$ can be either $9$ or $-9$ , we write two equations: $1$ . $x+6 = 9$ $2$ . $x+6 = -9$
Solve first equation: Solve the first equation $x+6 = 9$ . $\newline$ Subtract $6$ from both sides of the equation to isolate $x$ : $\newline$ $x + 6 - 6 = 9 - 6$ $\newline$ $x = 3$
Solve second equation: Solve the second equation $x+6 = -9$ . $\newline$ Subtract $6$ from both sides of the equation to isolate $x$ : $\newline$ $x + 6 - 6 = -9 - 6$ $\newline$ $x = -15$