In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

검증된 단계별 안내

Recall that the absolute value equation \(|A| = B\) can be rewritten as two separate equations: \(A = B\) and \(A = -B\), provided that \(B \geq 0\).

Identify \(A\) and \(B\) in the given equation \(|2x - 1| = 5\). Here, \(A = 2x - 1\) and \(B = 5\).

Set up the two equations based on the definition of absolute value: \(2x - 1 = 5\) and \(2x - 1 = -5\).

Solve each equation separately: For \(2x - 1 = 5\), add 1 to both sides and then divide by 2 to isolate \(x\). For \(2x - 1 = -5\), add 1 to both sides and then divide by 2 to isolate \(x\).

Write the two solutions you found as the solution set for the original absolute value equation.

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.

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any expression |A| = B, where B ≥ 0, the equation splits into two cases: A = B or A = -B. Understanding this definition is essential to solving absolute value equations.

Solving Linear Equations

Once the absolute value equation is split into two linear equations, solving each involves isolating the variable using inverse operations like addition, subtraction, multiplication, or division. Mastery of these steps is necessary to find the values of x that satisfy the original equation.

Checking for No Solution

If the absolute value equals a negative number, the equation has no solution because absolute values cannot be negative. Additionally, after solving, it is important to verify solutions in the original equation to ensure they are valid and not extraneous.