Classroom Resource

Solving Linear Inequalities with Negative Numbers

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.

Unpacked Content

UP:MA19.6.18

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.

Unpacked Content

UP:MA19.7.9

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

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility
License

License Type

PD

Comments or Notes

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

Approved Date

ALSDE LOGO

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