Example: Solving and Graphing $3(2x+5) \leq 18$ and $2(x-7) < -6$

Try It: Solving and Graphing $2(3x+1) \leq 20$ and $4(x-1) < 2$

A quality control technician is ensuring that a batch of medicine is stored within two safety temperature constraints. To find the final safe storage range, they must determine the values that satisfy both inequalities simultaneously (using 'and'). Arrange the following steps in the correct order to solve this problem.

A logistics manager at a distribution center is verifying that a shipping container's weight satisfies two separate safety constraints simultaneously (using 'and'). To find the final range of acceptable weights, they follow a standard three-step mathematical procedure. Match each step of this procedure with its corresponding action.

A quality control specialist is verifying that a precision-engineered bolt's diameter satisfies two different tolerance limits at the same time (joined by the word 'and'). According to the standard three-step mathematical procedure, after solving each individual inequality in Step 1, what is the specific objective of Step 2?

A quality control inspector is monitoring the thickness of a steel plate, which must satisfy two separate tolerance limits joined by the word 'and'. After independently solving each inequality and graphing the region where they overlap, the inspector follows the final step of the standard procedure by recording the solution set in standard ________ notation.

Solving Overlapping Constraints in Logistics

A data analyst is using the standard mathematical procedure to solve a compound inequality with the word 'and' to find a target demographic range. According to this procedure, the analyst should create the final graph by combining all values from the individual inequalities, even if the graphs do not overlap.

Try It: Solving and Graphing $3x - 4 < 5$ and $4x + 9 \geq 1$

Explaining the Procedure for Overlapping Constraints

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

Example: Solving and Graphing $5(3x-1) \leq 10$ and $4(x+3) < 8$