Unit 4 · Solving Linear Equations & Inequalities
Inequalities use the same solving moves as equations, with one extra rule: multiplying or dividing by a negative reverses the symbol.
From −2x > 8, divide by −2 and flip: x < −4. Check with a number: x = −5 works because −2(−5) = 10 > 8.
The set of points on one side of a boundary line, used to graph a two-variable inequality.
Example: y > x + 1 is the open half-plane above the line y = x + 1.
Try the prompt first. The steps stay folded until you ask to see them.
Solve −3x + 1 ≥ 10.
Watch for
Forgetting to reverse the inequality
Multiplying by a negative reverses order on the number line.
Fix: Test a point from your solution set.
Submit each answer to check it. The key is not shown until you do.
Solve 5(x − 2) ≤ 3x + 20 algebraically. Enter the solution as an inequality in x.
A tour bus can seat at most 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If a is adult tickets and c is child tickets, which system models a profit?
Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. Which inequality could be used to determine the number of dimes, d, she needs?
Always test one number from the solution set in the original inequality.
Graph a system of two linear inequalities and describe the feasible region.
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