solve the equation.

$\sqrt{2x - 5} = 3$

if there is no solution, use the $\varnothing$ symbol.

use the keypad to enter the answer in the box.

$x = \square$

Question

solve the equation.

$\sqrt{2x - 5} = 3$

if there is no solution, use the $\varnothing$ symbol.

use the keypad to enter the answer in the box.

$x = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Equations", "Extraneous Solutions" ], "new_concepts": [], "current_concepts": [ "Radical Equations", "Extraneous Solutions" ] } ## Square both sides of the equation $$ \begin{aligned} \sqrt{2x - 5} &= 3 \ (\sqrt{2x - 5})^2 &= 3^2 \ 2x - 5 &= 9 \end{aligned} $$ ## Isolate the variable x $$ \begin{aligned} 2x &= 9 + 5 \ 2x &= 14 \ x &= 7 \end{aligned} $$ ## Verify the solution $$ \begin{aligned} \sqrt{2(7) - 5} &= \sqrt{14 - 5} \ &= \sqrt{9} \ &= 3 \end{aligned} $$ Solve the equation. $\sqrt{2x - 5} = 3$ If there is no solution, use the $\varnothing$ symbol. Use the keypad to enter the answer in the box. $x =$ 7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Square both sides of the equation

Isolate the variable x

Verify the solution

Answer: