Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific
rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.
Arizona Academic Standards:
7.EE.B.4b
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
Common Core State Standards:
Math.7.EE.4b or 7.PAR.3.2
Kentucky Academic Standards (KAS):
7.EE.4.b
Mississippi College- and Career-Readiness Standards:
7.EE.4b
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Georgia Math and ELA Standards:
7.PAR.3.2
Construct algebraic inequalities to solve problems, leading to inequalities of the form px + q > r, px + q < r, px + q ? r, or px + q ? r, where p, q, and r are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
North Carolina - Standard Course of Study:
7.EE.4.b
Construct inequalities to solve problems by reasoning about the quantities.
Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.
Compare an algebraic solution process for equations and an algebraic solution process for inequalities.
Graph the solution set of the inequality and interpret in context.
New York State Next Generation Learning Standards:
7.PAR.2
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Note: The words leading to in the standard may require students to simplify or combine like terms on the same side of the equation before it is in the form stated in the standard.
Tennessee Academic Standards:
7.PAR.3.2
Solve contextual problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality on a number line and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. (Note that inequalities using >, <, =, = are included in this standard).
Wisconsin Academic Standards:
7.PAR.3.2
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.
Pennsylvania Core Standards:
CC.2.2.7.B.3
Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
Pennsylvania Core Standards:
M07.B-E.2.2.2
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.
Pennsylvania Core Standards:
M07.B-E.2.3.1
Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.
Florida - Benchmarks for Excellent Student Thinking:
MA.7.AR.2.1
Construct algebraic inequalities to solve problems, leading to inequalities of the form px + q > r, px + q < r, px + q ? r, or px + q ? r, where p, q, and r are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
Georgia Math and ELA Standards:
7.PAR.3.2
Construct algebraic inequalities to
solve problems, leading to
inequalities of the form px ± q > r,
px ± q < r, px ± q ≤ r, or px ± q ≥ r,
where p, q, and r are specific
rational numbers. Graph and
interpret the solution based on the
realistic situation that the
inequalities represent.
Arkansas Academic Standards:
7.ALG.3
Create, solve, and graph two-step inequalities in real-world and mathematical problems in the forms px ± q > r, px ± q < r, px ± q ≥ r, and px ± q ≤ r.
7th Grade Math - Linear Inequalities Lesson
Inequality Word Problems
Setting up an equation can be helpful for solving word problems. What if the word problem involves an inequality? Solving inequality word problems is similar; however, instead of setting up an equation, set up an inequality.
Example:
Set up an inequality to represent the situation and solve for the unknown value. The unknown value is the number of months Candice has had the puppy, which we will call x.
The amount of weight the puppy has gained each month is 4 pounds. So, the weight he has gained since Candice got him is 4 pounds times the number of months she has had him, or 4x. Then, as part of his current weight, add his original weight to 4x.
4x + 10
The puppy now weighs more than 30 pounds. So, write the expression with an inequality sign, greater than 30, and solve.
4x + 10
>
30
4x + 10 - 10
>
30 - 10
4x
>
20
4x ÷ 4
>
20 ÷ 4
x
>
5
So, Candice has had the puppy for more than 5 months.
Sometimes solutions to inequalities are represented on a number line. To use a number line representation, first, place an open circle on the tick mark at the maximum value (for less than) or minimum value (for greater than). Then, extend an arrow from the circle to the left or right, depending on if the solutions are less than or greater than that value, respectively.
Example:
Draw a number line with an open circle on the 5 tick mark.
Then, draw an arrow extending to the right.