1Cademy - Try It: Solving and Graphing $$ 4x - 7

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Procedure for Solving Compound Inequalities with "and"

Example

Try It: Solving and Graphing $4x - 7 < 9$ and $5x + 8 \geq 3$

To practice solving a compound inequality with "and", solve the inequalities $4x - 7 < 9$ and $5x + 8 \geq 3$ . Solving the first inequality gives $4x < 16$ , which simplifies to $x < 4$ . Solving the second inequality yields $5x \geq -5$ , which simplifies to $x \geq -1$ . Graphing both results shows that the intersection—the numbers making both true—is between $-1$ and $4$ . The boundary $-1$ is included while $4$ is not. In interval notation, this overlapping solution is written as $[-1, 4)$ .