Examples with solutions for Equations with Absolute Values: Solving an exercise

Exercise #1

x+4=10 \left|x+4\right|=10

Step-by-Step Solution

To solve the equation x+4=10 \left|x+4\right|=10 , we split it into two separate equations:

1. x+4=10 x+4=10

2. x+4=10 x+4=-10

For the first equation:

x+4=10 x+4=10

Subtract 4 from both sides:

x=6 x=6

For the second equation:

x+4=10 x+4=-10

Subtract 4 from both sides:

x=14 x=-14

Thus, the solutions are x=6 x=6 and x=14 x=-14 .

Answer

x=6 x=6 , x=14 x=-14

Exercise #2

2x+3=9 \left|2x+3\right|=9

Step-by-Step Solution

To solve the equation 2x+3=9 \left|2x+3\right|=9 , we split it into two separate equations:

1. 2x+3=9 2x+3=9

2. 2x+3=9 2x+3=-9

For the first equation:

2x+3=9 2x+3=9

Subtract 3 from both sides:

2x=6 2x=6

Divide both sides by 2:

x=3 x=3

For the second equation:

2x+3=9 2x+3=-9

Subtract 3 from both sides:

2x=12 2x=-12

Divide both sides by 2:

x=6 x=-6

Thus, the solutions are x=3 x=3 and x=6 x=-6 .

Answer

x=3 x=3 , x=6 x=-6

Exercise #3

3x5=12 \left|3x-5\right|=12

Step-by-Step Solution

To solve the equation 3x5=12 \left|3x-5\right|=12 , we split it into two separate equations:

1. 3x5=12 3x-5=12

2. 3x5=12 3x-5=-12

For the first equation:

3x5=12 3x-5=12

Add 5 to both sides:

3x=17 3x=17

Divide both sides by 3:

x=523 x=5\frac{2}{3}

For the second equation:

3x5=12 3x-5=-12

Add 5 to both sides:

3x=7 3x=-7

Divide both sides by 3:

x=213 x=-2\frac{1}{3}

Thus, the solutions are x=523 x=5\frac{2}{3} and x=213 x=-2\frac{1}{3} .

Answer

x=523 x=5\frac{2}{3} , x=213 x=-2\frac{1}{3}

Exercise #4

x1=6 \left|x-1\right|=6

Video Solution

Answer

x=5 x=-5 , x=7 x=7