Solving Linear Inequalities with Negative Numbers

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

6, 7

Overview

Solve an inequality that has negative numbers and a variable. This video focuses on using inverse operations to solve for a variable and the importance of flipping the inequality when multiplying or dividing by a negative number. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

Mathematics (2019) Grade(s): 6

MA19.6.18
Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.

Vocabulary

Substitution
Equation
Inequality

Knowledge

Students know:

Conventions of order of operations.
The solution is the value of the variable that will make the equation or inequality true.
That using various processes to identify the value(s) that when substituted for the variable will make the equation true.

Skills

Students are able to:

Substitute specific values into algebraic equation or inequality and accurately perform operations of addition, subtraction, multiplication, division and exponentiation using order of operation.

Understanding

Students understand that:

Solving an equation or inequality means finding the value or values (if any) that make the mathematical sentence true.
The solution to an inequality is often a range of values rather than a specific value.

Mathematics (2019) Grade(s): 7

MA19.7.9
Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

Vocabulary

Algebraic expressions
Equations
Inequalities
Greater than
Greater than or equal to
less than
less than or equal to

Knowledge

Students know:

p(x + q) = px + pq, where p and q are specific rational numbers.
When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( ).

Skills

Students are able to:

use variables to represent quantities in a real-world or mathematical problem.
Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
Construct simple inequalities (px + q > r or px + q
Graph the solution set of an inequality.

Understanding

Students understand that:

Real-world problems can be represented through algebraic expressions, equations, and inequalities.
Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD

https://aptv.pbslearningmedia.org/resource/mgbh.math.ee.inequality/solving-line…

Comments or Notes

Additional support materials are located under Support Materials for Teachers in the upper right-hand corner of the webpage.

Approved Date

2022-10-04

Design by Adaptive Theme