Solve each equation. |2x + 3/ 3x - 4 | = 1

Key Concepts

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number 'a', the absolute value is denoted as |a| and is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. In the context of equations, the absolute value can lead to two separate cases that must be solved individually.

Equations with Absolute Values

When solving equations involving absolute values, such as |A| = B, where B is a positive number, we create two separate equations: A = B and A = -B. This approach allows us to find all possible solutions that satisfy the original equation. It is crucial to check each solution in the context of the original equation to ensure they are valid.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. In the equation given, |(2x + 3)/(3x - 4)| = 1, understanding how to manipulate and simplify rational expressions is essential. This includes finding common denominators, factoring, and ensuring that the denominator does not equal zero, as this would make the expression undefined.