Solving Multi-step Inequalities

Solving and graphing multi-step inequalities

February 2023

Standard and Objectives

• I can determine the solution to an inequality with only positive numbers

• I can compare and contrast solutions to equations and solutions to inequalities

• NC.7.EE.4.b Construct inequalities to solve problems by reasoning about the quantities.
  o Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.
  o Compare an algebraic solution process for equations and an algebraic solution process for inequalities.
  o Graph the solution set of the inequality and interpret in context.

Multiple Choice

When you graph an inequality, you use a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

• ≤, <

• ≥, >

Multiple Choice

What inequality does the number line graph represent?

• x > 5

• x < −5

• x ≥ 5

• x ≥ −5

When the number you multiply or divide your variable by is positive, you solve inequalities the same way you solve equations

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​Solving two-step inequalities with positive numbers

Multiple Choice

What is the first step to solving this inequality?

$$9x\ -\ 6\ >\ 66$$  

• Add 9 to both sides of the inequality.

• Divide both sides of the inequality by 9.

• Subtract 6 on both sides of the inequality.

• Add 6 to both sides of the inequality.

Multiple Choice

What is the first step to solve the following inequality?

$$25\ -\ 4y\ \ge\ 37$$  

• Subtract 25 from both sides of the inequality.

• Add 25 to both sides of the inequality.

• Divide both sides of the inequality by 4.

• Multiply both sides of the inequality by -4.

Multiple Choice

How do we solve this inequality?

$$9\ -\ \frac{4}{5}x\ \le-3$$  

• Subtract 9, then multiply both sides by $$-\frac{5}{4}$$  

• Subtract 9, then multiply both sides by $$\frac{5}{4}$$

• Add 9, then multiply both sides by $$-\frac{5}{4}$$

• Add 9, then multiply both sides by $$-\frac{4}{5}$$

Multiple Choice

6(n + 2) < -72

• n < -14

• n < 11.667

• n < -10

• n < 14

Multiple Choice

Solve the inequality

• x ≤ -17

• x ≤ -11

• x ≤ 7

• x ≤ -35