Equation Solving Exit Ticket
Exit Ticket Algebra 1 • Multi-Step Equations
Solving Equations with Distribution
Score: _____ / 12 pts
Standard: HSA.REI.B.3
Name: ______________________
Date: __________________
Period: ________________
Directions: Solve each equation below. Show all algebraic steps clearly (distribute, collect variables, isolate the constant, and solve). Verify your solution in the check space.
1 Solve for \( x \):
4 points
\( 2(-4x + 5) = 14 - 6x \)
Show Step-by-Step Work
Check
\( x = \)
2 Solve for \( w \):
4 points
\( 5(-2w + 3) = 33 - 7w \)
Show Step-by-Step Work
Check
\( w = \)
3 Solve for \( y \):
4 points
\( 3(-3y - 4) = 8 - 5y \)
Show Step-by-Step Work
Check
\( y = \)
Self-Assessment: How confident do you feel?
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Teacher Guide & Key Multi-Step Equations Exit Ticket
Answer Key & Diagnostic Rubric
Full Solutions
Problem 1: \( 2(-4x + 5) = 14 - 6x \) Answer: \( x = -2 \)
Step-by-Step Solution
1. Distribute: \( -8x + 10 = 14 - 6x \)
2. Add \( 6x \): \( -2x + 10 = 14 \)
3. Subtract \( 10 \): \( -2x = 4 \)
4. Divide by \( -2 \): \( \mathbf{x = -2} \)
Check & Common Errors
Check: \( 2(-4(-2)+5) = 2(13) = 26 \); \( 14-6(-2) = 26 \checkmark \)
Common Mistake: Distributing 2 to only \( -4x \) and forgetting to multiply by 5 (\( -8x + 5 \)).
Problem 2: \( 5(-2w + 3) = 33 - 7w \) Answer: \( w = -6 \)
Step-by-Step Solution
1. Distribute: \( -10w + 15 = 33 - 7w \)
2. Add \( 7w \): \( -3w + 15 = 33 \)
3. Subtract \( 15 \): \( -3w = 18 \)
4. Divide by \( -3 \): \( \mathbf{w = -6} \)
Check & Common Errors
Check: \( 5(-2(-6)+3) = 5(15) = 75 \); \( 33-7(-6) = 75 \checkmark \)
Common Mistake: Sign error when dividing by negative coefficient (\( 18 / -3 \neq +6 \)).
Problem 3: \( 3(-3y - 4) = 8 - 5y \) Answer: \( y = -5 \)
Step-by-Step Solution
1. Distribute: \( -9y - 12 = 8 - 5y \)
2. Add \( 5y \): \( -4y - 12 = 8 \)
3. Add \( 12 \): \( -4y = 20 \)
4. Divide by \( -4 \): \( \mathbf{y = -5} \)
Check & Common Errors
Check: \( 3(-3(-5)-4) = 3(11) = 33 \); \( 8-5(-5) = 33 \checkmark \)
Common Mistake: Subtracting 12 instead of adding 12 to both sides when isolating.
4-Point Problem Rubric Total Exit Ticket: 12 Points
1 pt: Distribution
Correctly distributes multiplier across both terms inside parentheses.
1 pt: Variable Collection
Correctly moves variable terms to one side using inverse operations.
1 pt: Isolation & Solve
Isolates constant and correctly divides by the coefficient.
1 pt: Verification / Check
Substitutes solution back into the original equation to verify.