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Break down the given absolute value equation two separate equations.
w=- 2 and w=- 1/5
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 2(4w-1) ≥ 0:2(4w-1) = 3(4w+2) & (I) 2(4w-1) < 0:2(4w-1) = - 3(4w+2) & (II)
(I), (II):Distribute 2
(I), (II): Distribute 3
(II): Distribute -1
(I), (II): LHS+2=RHS+2
(I): LHS-12w=RHS-12w
(I): .LHS /(- 4).=.RHS /(- 4).
(II): LHS+12w=RHS+12w
(II): .LHS /20.=.RHS /20.
(II): a/b=.a /4./.b /4.
w= - 2
a(- b)=- a * b
Add and subtract terms
|-9|=9
|-6|=6
Multiply
w= - 1/5
a(- b)=- a * b
a* 1/b= a/b
Write as a fraction
Add and subtract fractions
|-9/5|=9/5
|6/5|=6/5
a*b/c= a* b/c