Equations with Absolute Values: Solving the problem

Question 1

$\left|6x-12\right|=6$

Question 2

$\left|x-10\right|=0$

Question 3

$\left|x+1\right|=5$

Question 4

$\left|x\right|=5$

Question 5

$\left|2x+6\right|=1$

Examples with solutions for Equations with Absolute Values: Solving the problem

Exercise #1

$\left|6x-12\right|=6$

Video Solution

Step-by-Step Solution

To solve this exercise, we need to note that the left side is in absolute value.

Absolute value checks the distance of a number from zero, meaning its solution is always positive.

Therefore, we have two possibilities, either the numbers inside will be positive or negative,

In other words, we check two options, in one what's inside the absolute value is positive and in the second it's negative.

6x-12=6

6x=18

x=3

This is the first solution

-(6x-12)=6
-6x+12=6
-6x=6-12
-6x=-6
6x=6
x=1

And this is the second solution,

So we found two solutions,

x=1, x=3

And that's the solution!

Answer

$x=1$ , $x=3$

Exercise #2

$\left|x-10\right|=0$

Video Solution

Answer

$x=10$

Exercise #3

$\left|x+1\right|=5$

Video Solution

Answer

Answers a + b

Exercise #4

$\left|x\right|=5$

Video Solution

Answer

Answers a + b

Exercise #5

$\left|2x+6\right|=1$

Video Solution

Answer

$x=-2.5$ , $x=-3.5$

Question 1

$\left|3x-12\right|=3$

Question 2

$\left|x+2\right|=4$

Question 3

$\left|x-3\right|=4$

Question 4

$\left|-x\right|=10$

Exercise #6

$\left|3x-12\right|=3$

Video Solution

Answer

$x=5$ , $x=3$

Exercise #7

$\left|x+2\right|=4$

Video Solution

Answer

$x=-6$ , $x=2$

Exercise #8

$\left|x-3\right|=4$

Video Solution

Answer

$x=-1$ , $x=7$

Exercise #9

$\left|-x\right|=10$

Video Solution

Answer

$x=-10$ , $x=10$