ACT Math · Number operations and exponents

Solve for x: √(2x - 3) = 5.

Solve for xx: 2x−3=5\sqrt{2x - 3} = 5.

Answer and explanation

Answer: A: 14

Square both sides to remove the radical: 2x−3=252x-3=25. Add 33: 2x=282x=28. Divide by 22: x=14x=14, choice A. Always check for extraneous solutions when squaring: 2(14)−3=25=5\sqrt{2(14)-3}=\sqrt{25}=5, which is correct. Choice D (2828) stops at 2x=282x=28 and does not divide by 22. Choice B (1111) subtracts 33 instead of adding it: 25−32=11\frac{25-3}{2}=11, which gives 19\sqrt{19}, not 55. Choice C (44) does not work: 2(4)−3=5\sqrt{2(4)-3}=\sqrt5, not 55. Squaring can introduce extra roots, so the check is always needed.

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