4. Solving Absolute Value Equations
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Break down the given absolute value equation two separate equations.
a=5/2 and a=1/2
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 6a-5 ≥ 0:6a-5 = 4a & (I) 6a-5 < 0:6a-5 = - 4a & (II)
LHS-6a=RHS-6a
(I):.LHS /(- 2).=.RHS /(- 2).
(II):.LHS /(-10).=.RHS /(-10).
Rearrange equation
(II):a/b=.a /5./.b /5.
a= 5/2
a*b/c= a* b/c
Calculate quotient
Subtract term
|10|=10
a= 1/2
a* 1/b= a/b
Calculate quotient
Subtract term
|-2|=2