facts about Absolute Value
If x is positive, | x | = x
If x is negative, | x | = -x
If x is positive, | x | = x, so the first equation to solve is x = 4. Done because x is automatically isolated
If x is negative, | x | = -x, so the second equation to solve is -x = 4.
You can write -x = 4 as -1x = 4 and divide both sides by -1 to isolate x.
(-1/-1)x = 4/-1
1x = -4
x = -4
Therefore, the solutions are 4 and -4
If x is positive, | x | = x
If x is negative, | x | = -x
If x is positive, | x | = x, so the first equation to solve is x = 4. Done because x is automatically isolated
If x is negative, | x | = -x, so the second equation to solve is -x = 4.
You can write -x = 4 as -1x = 4 and divide both sides by -1 to isolate x.
(-1/-1)x = 4/-1
1x = -4
x = -4
Therefore, the solutions are 4 and -4
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Follow these steps to solve an absolute value equality which contains one absolute value:
Follow these steps to solve an absolute value equality which contains one absolute value:
- Isolate the absolute value on one side of the equation.
- Is the number on the other side of the equation negative? If you answered yes, then the equation has no solution. If you answered no, then go on to step 3.
- Write two equations without absolute values. The first equation will set the quantity inside the bars equal to the number on the other side of the equal sign; the second equation will set the quantity inside the bars equal to the opposite of the number on the other side.
- Solve the two equations.
Examples:
_|4| = 4
|-4| = 4
|4+3| = 7
|-4-3| = 7
|3-4| = 1
-|4| = -4
-|-4| = -4
|-4| = 4
|4+3| = 7
|-4-3| = 7
|3-4| = 1
-|4| = -4
-|-4| = -4