Montana Math MT.8.EE.7
The Standard
Solve linear equations in one variable by: Giving examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions and showing which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers), and Solving linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve equations with fractions or decimals, including ones that need distributing and combining like terms. They simplify each equation to show whether it has one solution, every number as a solution, or no solution. They write an example of each type.
What Mastery Looks Like
- A student keeps both sides equal at each step and finds x when there is one solution. They know that 4 = 4 means every number works, while 4 = 7 means none do. They can create an equation that leads to each result.
Common Misconceptions
- Students may treat 3 = 3 as x = 3 instead of recognizing that every number works. They may think a false statement such as 3 = 5 has a solution. They also sometimes distribute to only the first term inside parentheses.
How to Assess It
- Exit ticket: Solve and classify 1/2(2x+4)=5, 2(x+1)=2x+2, and 3(x-1)=3x+1. Show each step and label each equation as having one solution, infinitely many solutions, or no solutions.
Lesson moves
Ways to Teach It
Use algebra tiles to build 2(x+1)=x+5, then remove matching tiles from both sides to find x.
Have pairs explain in writing why 2(x+1)=2x+2 works for every x but 2(x+1)=2x+3 works for none.
Give pairs three equation cards, one of each solution type, and have them sort the cards and show their steps.
Compare taxi fares of $4 plus $2.50 per mile and $10 plus $1.75 per mile, then solve when the costs match.
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Related Standards
- MT.7.EE.1
Use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients and generate equivalent expressions.
- MT.7.EE.3
Write and solve one- and two-step equations including problems in context with rational numbers, convert between forms as appropriate, and assess the reasonable...
- MT.8.EE.8
Analyze and solve pairs of simultaneous linear equations by: Understanding that solutions to a system of two linear equations in two variables correspond to poi...
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