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Chapter 1: Problem 92

$$\text { Solve }|2 x-3|=0$$.

Short Answer

Expert verified
x = \frac{3}{2}

Step by step solution

01

Understand the Absolute Value Equation

The given equation is \(|2x-3|=0\). An absolute value equation is equal to zero when the expression inside the absolute value is zero. Thus, we need to solve the equation inside the absolute value for zero.
02

Set the Expression Inside to Zero

Set the expression inside the absolute value equal to zero. This gives the equation: \(2x - 3 = 0\).
03

Solve for x

To solve \(2x - 3 = 0\), add 3 to both sides of the equation to get: \(2x = 3\). Then, divide both sides by 2 to isolate \x\: \(x = \frac{3}{2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving absolute value equations
Solving absolute value equations might seem tricky at first, but it gets easier with practice.
The equation \(|2x-3|=0\) is a good starting point to understand the basics.
Absolute value, represented by \(|...|\), essentially measures the distance of a number from zero on a number line.
This distance is always non-negative.
linear equations
When we deal with absolute value equations, they often simplify to solving a linear equation.
This is because we are trying to eliminate the absolute value by focusing on the expression inside it.
The given equation \(|2x-3|=0\) leads us to the linear equation \(2x - 3 = 0\).
Here, the goal is to isolate \(x\) by using basic algebraic operations.
precalculus problem solving
Precalculus often involves solving various types of equations, including absolute value equations.
The equation \( |2x-3| = 0 \) is a simple example to illustrate problem-solving steps.
Remember always to consider the meaning of absolute value and apply it consistently.
Once the absolute value is dealt with, solving the resulting linear equation becomes straightforward.

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