1Cademy - Solving $$\sqrt{2x-1} = 7$$

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Solving an Equation

Example

Solving $\sqrt{2x-1} = 7$

Solve the radical equation $\sqrt{2x - 1} = 7$ using the four-step procedure.

Step 1 — Isolate the radical. The square root $\sqrt{2x - 1}$ is already alone on the left side, so no rearrangement is needed.

Step 2 — Square both sides. Apply the Squaring Property to eliminate the radical:

$(\sqrt{2x - 1})^2 = 7^2$

$2x - 1 = 49$

Step 3 — Solve the new equation. Add $1$ to both sides: $2x = 50$ . Divide both sides by $2$ : $x = 25$ .

Step 4 — Check. Substitute $x = 25$ into the original equation:

$\sqrt{2(25) - 1} = \sqrt{50 - 1} = \sqrt{49} = 7$

Since $7 = 7$ is true, $x = 25$ is confirmed as the solution.

Updated 2026-04-21

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OpenStax Elementary Algebra

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