Question

Solve the following equation: |2x - 3|= 4x - 1

Answer 1

Hi there,

Happy to help! So let's get into it!

$|2x - 3| = 4x - 1$

The first step to take is to solve for the Absolute Value.

Thus, we know either $2x - 3 =4x-1$ or $2x-3=-(4x-1)$

So now let's solve both possibilities:

Possibility #1

$2x - 3 = 4x$

Subtract $4x$ from both sides

$2x - 3 -4x=4x-1-4x$

$-2x -3=-1\\-2x=-1+3\\-2x=2\\x = \frac{2}{-2} \\x = -1$

Now let's solve the second possibility

Possibility #2

$2x -3=-(4x-1)$

So basically here we need to simplify it. And we can start doing that by adding $4x$ to both sides

$2x - 3 + 4x = -4x +1+4x \\6x - 3 = 1\\6x = 1+3\\6x = 4 \\x = \frac{4}{6} \\x = \frac{2}{3}$

The answer is $x = \frac{2}{3}$

All the best this semester!

Answer 2

Answer: x=2/3

Step-by-step explanation:

|2x - 3|= 4x - 1

2x-3=4x-1

2x=4x+2

-2x=2

x=-1

4(-1)-1=

-4-1=-5 ==> Absolutes values can't equal a negative number

-(2x-3)=4x-1

-2x+3=4x-1

3=6x-1

6x=4

x=4/6

x=2/3