How do you solve $| 2 x - 5 | + 3 = 12$ $| 2x - 5 | + 3 = 12$ ?

Question

How do you solve $| 2 x - 5 | + 3 = 12$ $| 2x - 5 | + 3 = 12$ ?

2 Answers

Impact of this question

6042 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-03T00:11:49

$x = 7, - 2$ $x = 7, -2$

Explanation:

$| 2 x - 5 | + 3 = 12$ $|2x - 5| + 3 = 12$ Given Equation

$| 2 x - 5 | = 9$ $|2x - 5| = 9$ Subtracted $3$ $3$ from both sides

$| 2 x | = 14$ $|2x| = 14$ Added $5$ $5$ to each side.

$x = 7$ $x = 7$ Divided 2 by both sides

Since this is absolute value, you are also required to also solve the equation where in this case $x$ $x$ could also be negative aswell as positive.

$- | 2 x - 5 | + 3 = 12$ $-|2x - 5| + 3 = 12$

$- 2 x + 5 + 3 = 12$ $-2x + 5 + 3 = 12$ Distributed the negative sign.

$- 2 x + 8 = 12$ $-2x + 8 = 12$ Added 5 and 3.

$- 2 x = 4$ $-2x = 4$ Subtracted 8 from 12.

$x = - 2$ $x = -2$ Divided -2 to 4.

Answer 2 · 2018-03-03T00:22:18

$x = - 2, 7$ $x=-2,7$

Explanation:

Solve:

$| 2 x - 5 | + 3 = 12$ $abs(2x-5)+3=12$

Since $| a | = a and - a$ $abs(a)=a and -a$ , the equation can be broken into two equations:

$2 x - 5 + 3 = 12$ $2x-5+3=12$ and $- (2 x - 5) + 3 = 12$ $-(2x-5)+3=12$

Solve the first equation:

$2 x - 5 + 3 = 12$ $2x-5+3=12$

Simplify $(- 5 + 3)$ $(-5+3)$ to $- 2$ $-2$ .

$2 x - 2 = 12$ $2x-2=12$

Add $2$ $2$ to both sides of the equation.

$2 x = 12 + 2$ $2x=12+2$

Simplify.

$2 x = 14$ $2x=14$

Divide both sides by $2$ $2$ .

$x = \frac{14}{2}$ $x=14/2$

$x = 7$ $x=7$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the second equation:

$- (2 x - 5) + 3 = 12$ $-(2x-5)+3=12$

Expand.

$- 2 x + 5 + 3 = 12$ $-2x+5+3=12$

Simplify $(5 + 3)$ $(5+3)$ to $8$ $8$ .

$- 2 x + 8 = 12$ $-2x+8=12$

Subtract $8$ $8$ from $12$ $12$

$- 2 x = 12 - 8$ $-2x=12-8$

Simplify.

$- 2 x = 4$ $-2x=4$

Divide both sides by $- 2$ $-2$ .

$x = \frac{4}{- 2}$ $x=4/(-2)$

$x = - 2$ $x=-2$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$x = - 2, 7$ $x=-2,7$

Science

Math

Humanities

... and beyond

How do you solve $| 2 x - 5 | + 3 = 12$ $| 2x - 5 | + 3 = 12$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve |2x−5|+3=12| 2x - 5 | + 3 = 12?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you solve $| 2 x - 5 | + 3 = 12$ $| 2x - 5 | + 3 = 12$ ?