Virginia SOL 7.PFA.3.c
The Standard
Confirm algebraic solutions to linear equations in one variable.
Virginia Standards of Learning for Mathematics · The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students check a solved value by substituting it into the original equation. They simplify both sides and decide whether the values are equal.
What Mastery Looks Like
- Students substitute their solution into the original equation and simplify each side correctly. They state that the solution is confirmed only when both sides have the same value.
Common Misconceptions
- Students may check a value in their final step instead of the original equation. They may also substitute without parentheses, mishandle negative values, or stop after finding unequal results without revising their work.
How to Assess It
- Give the exit ticket: “A student says x = -3 solves 4x + 7 = -5. Confirm or reject the solution by showing both sides.”
Lesson moves
Ways to Teach It
Give students equation cards and solution tiles, then have them substitute each tile into the original equation to find matching pairs.
Ask, “Why should you check a solution in the original equation?” Students write two sentences and compare answers with a partner.
Play Check or Reject: teams substitute a proposed value, calculate both sides, and earn a point for a correct decision and explanation.
Use a phone plan equation, solve for the number of gigabytes, then substitute the answer to verify the stated monthly cost.
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Related Standards
- 8.PFA.4.g
The 8th Grade version of this standard.
- 8.PFA.4.f
Interpret algebraic solutions in context to linear equations in one variable.
- 8.PFA.5.g
Interpret algebraic solutions in context to linear inequalities in one variable.
- 7.PFA.4.c
Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.
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