# Algebra II : Solving Absolute Value Equations

## Example Questions

### Example Question #51 : Solving Absolute Value Equations

Solve the equation:

Explanation:

Break up the inequality and write out its positive and negative components.

Solve the first equation.  Subtract 3 from both sides.

Divide both sides by 2.

The first solution is:

Solve the second equation.  Divide the equation by negative one, which will move the negative sign from left to right.

Subtract three from both sides.

Divide by 2 on both sides.

### Example Question #52 : Solving Absolute Value Equations

Solve the equation:

Explanation:

Add 40 on both sides of the equation.

Split this absolute value into its positive and negative components.

For the first equation, divide by eight to isolate the x-variable.

For the second equation, divide by negative eight on both sides.

### Example Question #53 : Solving Absolute Value Equations

Solve the equation:

Explanation:

Simplify both sides.

Separate the equation into its positive and negative components and eliminate the absolute value.

Simplify the first equation by dividing both sides by negative nine.

Simplify the second equation.  Double negatives negate, turning the true sign to positive.

Divide by nine on both sides.

### Example Question #54 : Solving Absolute Value Equations

Solve for x:

Explanation:

Whatever is inside the absolute value brackets could either be positive or negative.

Positive:

Negative:

### Example Question #55 : Solving Absolute Value Equations

Solve for x:

Explanation:

First, divide both sides by -3:

Whatever is inside the absolute value brackets could be positive or negative.

Positive:

Negative:

Both of those answers may not work, however, so test both:

The only answer that works is -1.

### Example Question #56 : Solving Absolute Value Equations

Solve for x:

Explanation:

First, add 7 to both sides:

Whatever is inside the absolute value brackets could either be positive or negative:

### Example Question #57 : Solving Absolute Value Equations

Solve for x:

Explanation:

First subtract 7 from both sides:

divide both sides by 2

The expression inside the absolute value brackets could be positive or negative.

Positive:

Negative:

### Example Question #58 : Solving Absolute Value Equations

Solve for x:

No solution

No solution

Explanation:

The expression inside the absolute value brackets could be either positive or negative.

Positive:

subtract 5 from both sides

subtract 2x from both sides

Negative:

subtract 5 from both sides

divide both sides by 5

Now see if either actually works:

Neither actually works.

### Example Question #59 : Solving Absolute Value Equations

Solve for x:

Explanation:

First, add 3 to both sides:

Either the expression inside the brackets is positive or it is negative.

Positive: subtract 1 from both sides

subtract 2x from both sides

divide both sides by 2

Negative: subtract 1 from both sides

divide both sides by 6

Now check to be sure both actually work.

Both work.

### Example Question #60 : Solving Absolute Value Equations

Solve for x:

Explanation:

First, multiply both sides by 3:

The expression inside the absolute value brackets could either be positive or negative.

Positive: add 6x to both sides

divide both sides by 7

Negative: add 4 to both sides

subtract 6x from both sides

divide both sides by -5

Now test to see if both answers actually work.

so 1 does not work.