Solve for all values of x in simplest form. 12=|x-1| Answer: x=

Absolute Value Definition: We are given the equation 12 = |x - 1|. The absolute value function outputs the distance of a number from zero on the number line, which is always non-negative. Therefore, |x - 1| can be either 12 or -12 because the absolute value of both 12 and -12 is 12.Case when x - 1 is Positive: First, let's consider the case when x - 1 is positive or zero. We can remove the absolute value bars and solve the equation directly: x - 1 = 12 Now, add 1 to both sides of the equation to isolate x: x = 12 + 1 x = 13Case when x - 1 is Negative: Next, let's consider the case when x - 1 is negative. In this case, we need to consider the equation x - 1 = -12 because the absolute value of -12 is also 12. Now, add 1 to both sides of the equation to isolate x: x = -12 + 1 x = -11

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.

12=|x-1|
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $12=|x-1|$ $\newline$ 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

12=|x-1|

\newline

Answer:

x=

Absolute Value Definition: We are given the equation $12 = |x - 1|$ . The absolute value function outputs the distance of a number from zero on the number line, which is always non-negative. Therefore, $|x - 1|$ can be either $12$ or $-12$ because the absolute value of both $12$ and $-12$ is $12$ .
Case when $x - 1$ is Positive: First, let's consider the case when $x - 1$ is positive or zero. We can remove the absolute value bars and solve the equation directly: $\newline$ $x - 1 = 12$ $\newline$ Now, add $1$ to both sides of the equation to isolate $x$ : $\newline$ $x = 12 + 1$ $\newline$ $x = 13$
Case when $x - 1$ is Negative: Next, let's consider the case when $x - 1$ is negative. In this case, we need to consider the equation $x - 1 = -12$ because the absolute value of $-12$ is also $12$ . Now, add $1$ to both sides of the equation to isolate $x$ : $x = -12 + 1$ $x = -11$