Absolute Value Equations
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| Solve: |p|=2 | Since 2 is positive, |p|=2 is equivalent to p=2 or p=-2. To check, let p=2 and then p=-2 in the original equation.
<b>|p|=2 = |2|=2 = 2=2</b> True
<b>|p|=2 = |-2|=2 = 2=2</b> True
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| Solve: |5w+3|=7 | Think of the expression 5w+3 as X in the absolute value property. This would make X=7 or X=-7. Substitute X with 5w+3, then we have
<b>5w+3=7 = 5w=4 = w=4/5</b> or
<b>5w+3=-7 = 5w=-10 = w=-2</b>
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| Solve: |x/2 -1|=11 | <b>x/2-1=11 = 2(x/2-1)=2(11) = x-2=22 = x=24</b> or <b> x/2-1=-11 = 2(x/2-1)=2(-11) = x-2=-22 = x=-20</b>
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| Solve: |2x|+5=7 | Isolate the absolute value expression alone on one side of the equation, begin by subtracting 5 from both sides. Then apply the absolute value property. <b>|2x|+5=7 = |2x|=2</b> THEN <b>2x=2 = x=1</b> or <b>2x=-2 = x=-1</b>
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| Solve: |y|=0 | Look for all numbers whose distance from 0 is zero units. The only number is 0. <b>The solution is 0</b>
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| Solve: |x|=-5 | <b>There is no solution.</b> The absolute value of a number is never negative. I hope you did not try too hard.
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| Given two absolute value expressions, when are the absolute values of two expression equal? | Two absolute value expressions are equal when the expressions inside the absolute value bars are <b>equal to</b> or are <b>opposites</b> of each other.
Example <b>|2|=|2|</b> or <b>|-2|=|-2|</b> or <b>|-2|=|2|</b> or <b>|2|=|-2|</b>
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| Solve: |3x+2|=|5x-8| | <b>3x+2=5x-8 = -2x+2=-8 = -2x=-10 = x=5</b> or <b>3x+2=-(5x-8) = 3x+2=-5x+8 = 8x+2=8 = 8x=6 = x=3/4<b>
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| Solve: |x-3|=|5-x| | <b>x-3=5-x = 2x-3=5 = 2x=8 = x=4</b> or <b>x-3=-(5-x) = x-3=-5+x = x-3-x=-5+x-x = -3=-5 FALSE</b>
When an equation simplifies to a false statement, the equation has no solution. Thus, the only solution for the original absolute value equation is <b>4</b
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| Define the absolute value of variable x and its distance from zero if |x|=3 | All numbers whose distance from 0 is 3 units. Only two numbers are 3 units away from 0. <b>3</b> and <b>-3</b>
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| How do you type absolute value brackets? Example <i>|</i><b>x</b><i>|</i> | Hold the <b>SHIFT</b> key and press <b>FORWARD SLASH<b>
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