Solve the equation for all values of x. |x-1|-4=2x Answer: x=

Consider Two Cases: We have the equation |x-1|-4=2x. To solve it, we need to consider two cases because the absolute value function |x-1| can be positive or negative.Case 1: Positive or Zero: Case 1: When x-1 is positive or zero, |x-1| = x-1. So the equation becomes: (x-1) - 4 = 2x Now, we solve for x.Simplify Case 1: Simplify the equation from Case 1: x - 1 - 4 = 2x x - 5 = 2x Subtract x from both sides: -5 = xCheck Case 1: Check if x = -5 satisfies the original equation: |(-5)-1|-4=2(-5) |-6|-4=-10 6-4=-10 This is not true, so x = -5 is not a solution.Case 2: Negative: Case 2: When x-1 is negative, |x-1| = -(x-1). So the equation becomes: -(x-1) - 4 = 2x Now, we solve for x.Simplify Case 2: Simplify the equation from Case 2: -(x-1) - 4 = 2x -x + 1 - 4 = 2x -x - 3 = 2x Add x to both sides: -3 = 3x Divide by 3: x = -1Check Case 2: Check if x = -1 satisfies the original equation: |(-1)-1|-4=2(-1) |-2|-4=-2 2-4=-2 This is true, so x = -1 is a solution.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation for all values of
x.

|x-1|-4=2x
Answer:
x=

Solve the equation for all values of $x$ . $\newline$ $|x-1|-4=2 x$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve the equation for all values of

x

\newline

|x-1|-4=2 x

\newline

Answer:

x=

Consider Two Cases: We have the equation $|x-1|-4=2x$ . To solve it, we need to consider two cases because the absolute value function $|x-1|$ can be positive or negative.
Case $1$ : Positive or Zero: Case $1$ : When $x-1$ is positive or zero, $|x-1| = x-1$ . So the equation becomes: $\newline$ $(x-1) - 4 = 2x$ $\newline$ Now, we solve for $x$ .
Simplify Case $1$ : Simplify the equation from Case $1$ : $\newline$ $x - 1 - 4 = 2x$ $\newline$ $x - 5 = 2x$ $\newline$ Subtract $x$ from both sides: $\newline$ $-5 = x$
Check Case $1$ : Check if $x = -5$ satisfies the original equation: $\newline$ $|(-5)-1|-4=2(-5)$ $\newline$ $|-6|-4=-10$ $\newline$ $6-4=-10$ $\newline$ This is not true, so $x = -5$ is not a solution.
Case $2$ : Negative: Case $2$ : When $x-1$ is negative, $|x-1| = -(x-1)$ . So the equation becomes: $\newline$ $-(x-1) - 4 = 2x$ $\newline$ Now, we solve for $x$ .
Simplify Case $2$ : Simplify the equation from Case $2$ : $\newline$ $- (x - 1) - 4 = 2x$ $\newline$ $-x + 1 - 4 = 2x$ $\newline$ $-x - 3 = 2x$ $\newline$ Add $x$ to both sides: $\newline$ $-3 = 3x$ $\newline$ Divide by $3$ : $\newline$ $x = -1$
Check Case $2$ : Check if $x = -1$ satisfies the original equation: $\newline$ $|(-1)-1|-4=2(-1)$ $\newline$ $|-2|-4=-2$ $\newline$ $2-4=-2$ $\newline$ This is true, so $x = -1$ is a solution.