Example: Solving and Graphing $9y + 2(y + 6) > 5y - 24$

Example: Solving and Graphing $6u + 8(u - 1) > 10u + 32$

Example: Solving and Graphing $4b - 3(3 - b) > 5(b - 6) + 2b$

Solving the Linear Inequality $2a < 5a + 12$

A logistics coordinator is using the inequality ${}-2x + 400 \leq 100$ to determine the maximum number of additional crates, $x$, that can be added to a shipment without exceeding a weight limit. To isolate $x$ in the final step of the solution, the coordinator must divide both sides by -2. Which rule must be recalled when performing this operation?

A production manager is solving a multi-step linear inequality to determine the minimum number of units a factory must produce to stay within a specific budget. Arrange the following steps in the standard order typically used to solve a multi-step linear inequality for a variable, such as ${}x$.

A procurement officer is solving the inequality $-5x + 1200 \leq 400$ to stay within a quarterly budget for office supplies, where $x$ represents the number of units ordered. After simplifying the inequality to $-5x \leq -800$, the officer must divide both sides by $-5$ to solve for $x$. True or False: In this final step, the inequality sign $\leq$ must be reversed to $\geq$ to maintain the correct solution.

Simplifying Multi-Step Inequalities

A business operations manager is solving a multi-step linear inequality to determine the maximum number of safety inspections that can be performed within a fixed quarterly budget. Match each algebraic property or rule to the correct description of its role in the solution process.

An inventory analyst is solving a multi-step linear inequality to ensure warehouse storage costs remain under a specified budget. In the final step of the calculation, they must divide both sides of the inequality by a negative number to isolate the variable. To maintain a true statement, the analyst must ________ the direction of the inequality sign.

Budget Calculation Review

Example: Solving and Graphing $8x - 2(5 - x) < 4(x + 9) + 6x$

Example: Solving and Graphing $8p + 3(p - 12) > 7p - 28$

Example: Solving the Inequality $4x + 3 > 23$