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# Absolute Value Equa

### Absolute Value Equations

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
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>
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>
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>
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>
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.
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>
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>
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
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>
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>
Created by: 1588162190