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How do you solve #abs(15x-72) + 3.14 = 275#?

Answer 1

Isaiah Anthony

Two cases:

a. (15x - 72) + 3.14 = 275 15 x = 343.86 -> x = 22.92

b. -15x + 72 + 3.14 = 275 15x = 75.14 - 275 = -199.86 -> x = -13.32

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Answer 2

Hazel Anglin

To solve the equation abs(15x-72) + 3.14 = 275:

Subtract 3.14 from both sides to isolate the absolute value term: abs(15x-72) = 271.86.
Remove the absolute value by considering two cases: a) 15x - 72 is positive: 15x - 72 = 271.86. b) 15x - 72 is negative: -(15x - 72) = 271.86.
Solve each case separately: a) 15x - 72 = 271.86. Add 72 to both sides: 15x = 343.86. Divide both sides by 15: x = 22.924. b) -(15x - 72) = 271.86. Distribute the negative sign: -15x + 72 = 271.86. Subtract 72 from both sides: -15x = 199.86. Divide both sides by -15: x = -13.324.

So, the solutions are x = 22.924 and x = -13.324.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.