1Cademy - Solving $$3q \geq 7q

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Division Property of Inequality

Example

Solving $3q \geq 7q - 23$

Solve the multi-step linear inequality $3q \geq 7q - 23$ by collecting the variable terms together.

Step 1 — Collect the variables on the left side: Subtract $7q$ from both sides: $3q - 7q \geq -23$ $-4q \geq -23$

Step 2 — Isolate the variable: Divide both sides by $-4$ . Because you are dividing by a negative number, the inequality sign must reverse: $q \leq \frac{-23}{-4}$ $q \leq \frac{23}{4}$

Step 3 — Write the solution in interval notation: The solution includes $\frac{23}{4}$ and all real numbers less than it, which is written as $(-\infty, \frac{23}{4}]$ .