Writing and Solving One-Step Inequalities

Warm Up 1. 2. 3. 4.

When adding or subtracting the same number on both sides of an inequality, the inequality symbol remains the same. When multiplying or dividing by the same positive number on both sides of an inequality, the inequality symbol remains the same. When multiplying or dividing by the same negative number on both sides of an inequality, the inequality symbol reverses. To check the solution of the graph of an inequality, choose a number from the shaded part of the number line to substitute into the inequality.

Fiona solves this inequality: -4x > -8 She says that 2 and all numbers greater than 2 are solutions. Is Fiona’s answer correct? If not, for what inequality would Fiona’s answer be correct? Justify your answer.

Solve each inequality. Graph and check your solution. x – 11 < -7 9 ≤ y + 7

Graphing a Solution The graph helps you see values to use when checking your solution. The shaded values that are part of the number line and the value at a closed circle should make the inequality true.

Rewrite Inequalities with the Variable on the Left It is generally easier to read and understand this way. Once an inequality is simplified with the variable on the left, the inequality symbol indicates which way to shade the graph of the solution. Before moving the inequality symbol, check which side is oriented toward the variable. That side should be oriented toward the variable after the symbol is moved. For example: 9 > x, the closed side is oriented toward x, the same as x < 9.

Solve each inequality. Graph and check your solution. 1>− 𝑦 6 3x ≤ 6

Every month, Tracie writes a check for $25 to pay off part of a loan Every month, Tracie writes a check for $25 to pay off part of a loan. She has enough in her checking account to pay no more than $450 towards the loan. For how many months can Tracie send payments for the loan?

Let a ≤ 2 and a ≥ -2. Between what two values will the solution to ay < 6 be found? Justify your answer and graph it on a number line.

A submarine descends from sea level to the entrance of an underwater cave. The elevation of the entrance is -120 feet. The rate of change in the submarine’s elevation is no greater than -12 feet per second. Can the submarine reach the entrance to the cave in less than 10 seconds? Explain.

Selena has $10. What is the greatest amount of spinach she can buy? Gary has enough money to buy at most 5.5 pounds of potatoes. How much money does Gary have? Florence wants to spend no more than $3 on onions. Will she be able to buy 2.5 pounds of onions? Explain.

Exit Ticket Write the resulting inequality. -3 ≤ 6 Add 8 to both sides. 2. 2 > -4 Multiply both sides by -3. Solve each inequality. Graph and check the solution. 3. x + 8 > 3 4. -9x ≤ 18 5. To cover her rectangular screened in porch with outdoor carpet, Kendra needs at least 67.1 square feet of carpet. The length of Kendra’s porch is 12.2 feet. Write and solve an inequality to find the possible widths of Kendra’s porch?