HSA.REI.A.1: Explain equation solving steps — Practice

Work through problems with immediate feedback

Recall / Warm-Up

Which statement correctly describes what it means to solve an equation?

Find all values of the variable that make the equation true.

Simplify the expression on each side until they look the same.

Move all numbers to one side and all variables to the other.

Find a value that makes the left side as large as possible.

A student solves $x + 5 = 12$ and gets $x = 7$ . Which step correctly checks this answer?

Subtract 5 from both sides again: $7 - 5 = 2$ . Since $2 \neq 12$ , check again.

Substitute $x = 7$ into the original equation: $7 + 5 = 12$ . Since $12 = 12$ , it checks.

Since $7 < 12$ , the answer is confirmed.

Substitute $x = 7$ into the left side only: $7 + 5 = 12$ . Done.

Which of the following is an equation (not just an expression)?

$4x - 1 = 11$

$2(x - 4)$

$3x + 5$

$x^2 + 2x$

Fluency Practice

Which property of equality is used in this step?

$3x = 12 \;\Rightarrow\; x = 4$

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

Which property of equality is used in this step?

$x - 7 = 3 \;\Rightarrow\; x = 10$

Division Property of Equality

Subtraction Property of Equality — 7 was subtracted from both sides

Addition Property of Equality — 7 was added to both sides

Multiplication Property of Equality

A student writes the following step while solving an equation:

$2x - 6 + 4x = 3x + 12 \;\Rightarrow\; 6x - 6 = 3x + 12$

What is the correct justification for this step?

Addition Property of Equality

Division Property of Equality

Distributive Property

Simplify (combine like terms)

$A two-column proof table with three rows. Row 2 has a blank gray placeholder in the Reason column.$

In a two-column justification, a student writes these three lines. What property belongs in the blank?

Line 1: $5(2x + 1) - 3 = 3x + 27$ — Reason: Given
Line 2: $10x + 5 - 3 = 3x + 27$ — Reason: ???
Line 3: $10x + 2 = 3x + 27$ — Reason: Simplify

Subtraction Property of Equality

Multiplication Property of Equality

Addition Property of Equality

Distributive Property

Solve $4x - 7 = 2x + 11$ and write a two-column justification for each step. Use these property names where applicable: Addition Property of Equality, Subtraction Property of Equality, Division Property of Equality, Distributive Property, Simplify. Your last row should verify the solution.

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Exercises: Explain Each Step in Solving an Equation

Recall / Warm-Up

Fluency Practice