Solving Linear Equations and Inequalities

Solving Linear Equations and Inequalities

Linear equations in one variable are fundamental to the GED exam.

Standard Form

$$ax + b = c$$

4-Step Solution Strategy

1. Simplify: Distribute parentheses and combine like terms on both sides.
2. Collect Variables: Add or subtract variable terms to get them on one side.
3. Collect Constants: Add or subtract constant terms to get them on the opposite side.
4. Isolate Variable: Multiply or divide by the variable's coefficient.

Critical Inequality Rule

Golden Rule for Inequalities: Whenever you multiply or divide both sides by a negative number, you MUST reverse the inequality sign ($<$ becomes $>$, and $\le$ becomes $\ge$).

Worked Example:

Solve for $x$: $$-3x + 7 \le 22$$

1. Subtract 7: $$-3x \le 15$$
2. Divide by -3 and flip sign: $$x \ge -5$$