step 1 The absolute value of 2x minus 3 equals 4. Well, that means that this 2x minus 3 could be negati

Question

Solve. $$ |2 x-3|=4 $$

Name: Problem 27, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-05-15T16:10:41-08:00
Duration: 44 s
Channel: Cory Kuzinski
Description: Solve. |2 x-3|=4

   Solve.
$$
|2 x-3|=4
$$

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 8, Problem 27

Instant Answer

Solved by Expert Cory Kuzinski

05/15/2020

Step 1

Therefore, the absolute value of a number can either be positive or negative. So, we can set up two equations from $|2x-3|=4$: $$2x-3=4$$ and $$2x-3=-4$$ Show more…

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Solve. $$ |2 x-3|=4 $$

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Key Concepts

Linear Equations

After breaking an absolute value equation into different cases, the resulting equations are often linear. Solving these linear equations using algebraic methods such as addition, subtraction, multiplication, or division is essential in finding the solution to the original equation.

Case Analysis

When solving equations involving absolute value, the equation is typically split into two separate cases to account for the scenarios where the expression inside the absolute value is positive or negative. This approach is fundamental in handling the piecewise nature of absolute value functions.

Absolute Value

The absolute value of a number measures its distance from zero on the number line without regard to its direction. It is a key concept in understanding how signs affect numbers and is used extensively in various areas of mathematics.

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