Solve each equation. √4x-2 = √3x+1

검증된 단계별 안내

Start by writing the given equation clearly: $\sqrt{4x - 2} = \sqrt{3x + 1}$.

To eliminate the square roots, square both sides of the equation: $(\sqrt{4x - 2})^2 = (\sqrt{3x + 1})^2$.

Simplify both sides after squaring: $4x - 2 = 3x + 1$.

Isolate the variable $x$ by subtracting \$3x$ from both sides and adding $2$ to both sides: $4x - 3x = 1 + 2$.

Solve the resulting linear equation for $x$: $x = 3$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Square Roots and Radicals

Square roots represent a value that, when multiplied by itself, gives the original number. Understanding how to manipulate and simplify square root expressions is essential for solving equations involving radicals.

Isolating and Squaring Both Sides

To solve equations with square roots, isolate the radical expressions and then square both sides to eliminate the square roots. This step often transforms the equation into a polynomial form that is easier to solve.

Checking for Extraneous Solutions

Squaring both sides can introduce solutions that do not satisfy the original equation. It is important to substitute solutions back into the original equation to verify their validity and discard any extraneous roots.