Solve the equation .
Solve the equation by following steps:
step0: Solve for :
step1: Move the constant to the right side:
step2: Subtract the numbers:
step3: Separate into possible cases:
step4: Solve the equation:
step5: Rewrite:
The solutions to the equation are and .
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The Deep Dive
To solve , first, subtract 2 from both sides to isolate the absolute value: .
Now, remember that the expression inside absolute value could result in two cases:
which gives us
which gives us
So, the solutions are and .
Now go out there and check these values back in the original equation to ensure they fit! How cool is it that simple numbers can take you on a quest where you discover both solutions?