Substituting A Given Value For A Variable

Substituting A Given Value For A Variable

Variables

Opening

Variables

Equations and inequalities may contain one or more variables. When you substitute a value for a variable in an equation or inequality, the equation or inequality becomes either true or false.

Look at the balance scale in the interactive. It shows the expression x + 5 on the left and the expression 2x + 3 on the right.

  • Substitute 5 for each x in the expressions. What happens when = 5?
    • Is the equation + 5 = 2+ 3 true?
    • Is the inequality + 5 > 2+ 3 true?
    • Is the inequality + 5 < 2+ 3 true?

INTERACTIVE: Balance Scale X

Math Mission

Opening

Determine whether a given number is a solution to an equation or to an inequality.

Solution or Not?

Work Time

Solution or Not?

When a given number is substituted for a variable in an equation or an inequality, and the resulting equation or inequality is true, that number is a solution to the equation or inequality.

NOTE: Ignore the instructions on the interactive and follow the steps below.

  • Is 2 a solution to 2x + 5 = x + 7?
  • Check your answer by substituting 2 for each x on the balance scale. Does the scale become balanced?

INTERACTIVE: Balance Scale X

Match the Solution

Work Time

Match the Solution

  • For which equation or inequality is x = 4 a solution?

x + 5 = 3x + 1

+ 5 > 3+ 1

+ 5 < 3+ 1

  • Check your answer by using the Balance Scale X interactive. (Ignore the instructions on the interactive and follow these steps.) Represent the expression x + 5 on the left side and the expression 3+ 1 on the right side. Then subsitute 4 for each x on the scale.

INTERACTIVE: Balance Scale X

Solution of 2

Work Time

Solution of 2

  • Make an equation that contains five instances of and has the solution 2. Set up the equation so the instances of are not all on the same side.
  • Check your answer by substituting 2 for each in your equation.
  • Check your answer by setting up a balance scale that represents your equation and substituting 2 for each x

INTERACTIVE: Balance Scale X

Prepare a Presentation

Work Time

Prepare a Presentation

  • Select one of the Work Time problems.
  • Be prepared to justify the solution to the equation or inequality.

Challenge Problem

  • Use the balance scale to find as many solutions as you can to the inequality x + 7 <  2x + 1.
  • What can you conclude about the solutions to this inequality?

INTERACTIVE: Balance Scale X

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the ways that your classmates justified the solution to the equation or inequality they chose.

Find Solutions

Work Time

Find Solutions

Identify the solution(s) for each equation or inequality from the list provided. There may be more than one solution.

  1. + 2 = 7

    • 2          
    • 212
    • 5
  2. > 5

    • 4          
    • 8          
    • 4.5
  3. + 6 = 6 + x

    • 23          
    • 5          
    • 8
  4. 2x

    • 3          
    • 6.2          
    • 512
  5. + 4 + 5x < 8 + 2x

    • 5          
    • 9          
    • 12

Solving With Substitution

Formative Assessment

Summary of the Math: Solving With Substitution

Write a summary about solutions to equations and inequalities.

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

An equation can either be true or false because …