Wyoming Math 8.EE.7b
The Standard
Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. Recognize the three types of solutions to linear equations: one solution, infinitely many solutions, or no solutions.
2023 Wyoming Mathematics Content and Performance Standards · Analyze and solve linear equations and pairs of simultaneous linear equations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve multi-step equations and inequalities with parentheses and variables on both sides. They decide whether an equation has one solution, no solution, or infinitely many solutions.
What Mastery Looks Like
- A student solves 2(x+3)=x+10 and gets x=4. They can explain why 4x+2=4x+2 has infinitely many solutions, while 4x+2=4x+3 has none. They reverse the inequality sign when dividing by a negative.
Common Misconceptions
- Students may distribute to only one term inside parentheses or combine terms from opposite sides of an equation. They may forget to reverse an inequality sign when dividing by a negative. Some label both 0=0 and 0=1 as no solution.
How to Assess It
- Give an exit ticket: Solve 2(x+3)=x+10 and -2(x-1)>8. Then label 3(x+2)=3x+6 and 3(x+2)=3x+7 by their number of solutions.
Lesson moves
Ways to Teach It
Use algebra tiles to build 2(x+3)=x+10, then remove matching tiles from both sides until x is alone.
Ask students to write why 3(x+2)=3x+6 works for every x, while 3(x+2)=3x+7 works for none.
Have pairs sort equation cards into one, none, or infinitely many solutions, then solve each card to check their choices.
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Printable 8.EE.7b Worksheet
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Related Standards
- 8.EE.8b
Solve systems of two linear equations in two variables with integer solutions by graphing the equations.
- 7.EE.4d
Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.
- 7.EE.4c
Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning.
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