4. Solving Absolute Value Equations
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Break down the given absolute value equation two separate equations.
x=7 and x=- 3
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 3(x-4) ≥ 0:3(x-4) = (2x+5) & (I) 3(x-4) < 0:3(x-4) = - (2x+5) & (II)
x= - 3