Multi-Step Equations Guided Notes
Unit 4 • Expressions & Equations Algebra 1 / Pre-Algebra
Solving Multi-Step Equations
Guided Notes & Practice • Distributive Property & Combining Like Terms
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The 3-Step Strategy Checklist
Standard Solving Procedure
1
Distribute (DP)
Clear parentheses by multiplying: \( a(b + c) = ab + ac \)
2
Combine (CLT)
Group like terms on the same side of the equals sign.
3
Isolate Variable
Use inverse operations to solve for the unknown variable.
Part 1
Equations with the Distributive Property (DP)
Solve each equation. Show all steps.
Example 1
\( 3(x + 4) = 27 \)
Solution: \( x = \)
Example 2
\( -4(2m - 1) = 28 \)
Solution: \( m = \)
Example 3
\( 6(2y - 5) = 18 \)
Solution: \( y = \)
Part 2
Equations with Combining Like Terms (CLT)
Solve each equation. Show all steps.
Example 4
\( 6x - 14 + 2x = 34 \)
Solution: \( x = \)
Example 5
\( 19 = 9w - 4w - 6 \)
Solution: \( w = \)
Example 6
\( 7p + 18 - 11p = 2 \)
Solution: \( p = \)
Unit 4: Expressions & Equations • Guided Notes Page 1 of 2 • Continue to Page 2
Part 3
Equations with Both DP and CLT
Solve each equation. Show all steps.
Example 7
\( 3(2x + 4) + 5x = 45 \)
Solution: \( x = \)
Example 8
\( 8y - 2(3y - 5) = 24 \)
Solution: \( y = \)
Example 9
\( -4(p + 2) + 7p = 10 \)
Solution: \( p = \)
Example 10
\( 2(4m - 3) + 3(m + 4) = 50 \)
Solution: \( m = \)
Part 4
Spot the Error!
Analyze the work below, describe the mistake, and solve correctly.
Frankie solved: \( 5(x - 2) + 3x = 22 \)
Line 1: \( 5x - 2 + 3x = 22 \)
Line 2: \( 8x - 2 = 22 \)
Line 3: \( 8x = 24 \implies x = 3 \)
Describe Frankie's mistake:
Correct Solution Show all work
Correct Answer: \( x = \)
Unit 4: Expressions & Equations • Guided Notes Page 2 of 2 • Teacher Check: [ ] Complete [ ] Revise
