4. Solving Absolute Value Equations
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Break down the given absolute value equation two separate equations.
k=6 and k=-2/5
When solving an equation involving absolute value expressions, we should consider what would happen if we removed the absolute value symbols. Let's look at an example equation. |ax+b|=|cx+d| Although we can make 4 statements about this equation, there are actually only two possible cases to consider.
Statement | Result |
---|---|
Both absolute values are positive. | ax+b=cx+d |
Both absolute values are negative. | -(ax+b)=-(cx+d) |
Only the left-hand side is negative. | -(ax+b)=cx+d |
Only the right-hand side is negative. | ax+b=-(cx+d) |
lc 3k-2 ≥ 0:3k-2 = 2(k+2) & (I) 3k-2 < 0:3k-2 = - 2(k+2) & (II)
k= 6
Multiply
Add and subtract terms
|8|=8
Multiply
|16|=16
k= -2/5
a*b/c= a* b/c
Rewrite 2 as 10/5
Add and subtract fractions
|-16/5|=16/5
|8/5|=8/5
a*b/c= a* b/c