4. Solving Absolute Value Equations
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Break down the given absolute value equation two separate equations.
h=0.25
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 3h+1 ≥ 0:3h+1 = 7h & (I) 3h+1 < 0:3h+1 = - 7h & (II)
LHS-3h=RHS-3h
(I):.LHS /4.=.RHS /4.
(II):.LHS /(-10).=.RHS /(-10).
Rearrange equation
h= 1/4
a* 1/b= a/b
Rewrite 1 as 4/4
Add fractions
|7/4|=7/4
h= -1/10
a* 1/b= a/b
Rewrite 1 as 10/10
Add fractions
|7/10|=7/10