Solve each equation. |x + 1 | = |1 -3x|

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for solving equations involving absolute values, as it leads to the creation of two separate cases to consider.

Setting Up Cases

When solving equations that involve absolute values, it is essential to set up cases based on the definitions of absolute value. For the equation |A| = |B|, we can derive two scenarios: A = B and A = -B. This approach allows us to explore all possible solutions that satisfy the original equation.

Solving Linear Equations

Linear equations are equations of the first degree, meaning they involve variables raised only to the power of one. To solve these equations, we isolate the variable on one side of the equation. Understanding how to manipulate and solve linear equations is fundamental in finding the values of x that satisfy the conditions set by the absolute value equations.