Solve for all values of x in simplest form. |(x)/(5)|=12 Answer: x=

Understand absolute value equation: Understand the absolute value equation |(x)/(5)|=12. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the equation |(x)/(5)|=12 means that the distance of (x)/(5) from zero is 12. This can happen in two ways: either (x)/(5) is 12 or (x)/(5) is -12.Set up two equations: Set up two separate equations to solve for x. Since |(x)/(5)|=12 can mean (x)/(5) is 12 or (x)/(5) is -12, we write: 1. (x)/(5) = 12 2. (x)/(5) = -12Solve first equation: Solve the first equation (x)/(5) = 12. To find x, multiply both sides of the equation by 5: x = 12 * 5 x = 60Solve second equation: Solve the second equation (x)/(5) = -12. Similarly, multiply both sides of this equation by 5: x = -12 * 5 x = -60Combine solutions: Combine the solutions from Step 3 and Step 4. The solutions to the equation |(x)/(5)|=12 are x = 60 and x = -60.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of
x in simplest form.

|(x)/(5)|=12
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $\left|\frac{x}{5}\right|=12$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

\left|\frac{x}{5}\right|=12

\newline

Answer:

x=

Understand absolute value equation: Understand the absolute value equation $\left|\frac{x}{5}\right|=12$ . The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the equation $\left|\frac{x}{5}\right|=12$ means that the distance of $\frac{x}{5}$ from zero is $12$ . This can happen in two ways: either $\frac{x}{5}$ is $12$ or $\frac{x}{5}$ is $-12$ .
Set up two equations: Set up two separate equations to solve for $x$ . Since $\left|\frac{x}{5}\right|=12$ can mean $\frac{x}{5}$ is $12$ or $\frac{x}{5}$ is $-12$ , we write: $1$ . $\frac{x}{5} = 12$ $2$ . $\frac{x}{5} = -12$
Solve first equation: Solve the first equation $(x)/(5) = 12$ . $\newline$ To find $x$ , multiply both sides of the equation by $5$ : $\newline$ $x = 12 \times 5$ $\newline$ $x = 60$
Solve second equation: Solve the second equation $(x)/(5) = -12$ . Similarly, multiply both sides of this equation by $5$ : $x = -12 \times 5$ $x = -60$
Combine solutions: Combine the solutions from Step $3$ and Step $4$ . $\newline$ The solutions to the equation $\left|\frac{x}{5}\right|=12$ are $x = 60$ and $x = -60$ .