Sign Trap Warmup Worksheet
SIGN TRAP WARMUP
Multi-Step Equations & Distributive Safety
Name:
Date:
Period:
Mission: Choose the mathematically correct first step on the left, then solve fully in the workspace on the right.
QUESTION 1 Solve the equation:
\[-3(2x - 5) + 4x = 29\]
Select correct first step:
\( -6x - 5 + 4x = 29 \)
\( -6x - 15 + 4x = 29 \)
\( -6x + 15 + 4x = 29 \)
\( -6x + 15 - 12x = 29 \)
MY WORKSPACE
QUESTION 2 Solve the equation:
\[5 - 2(4w - 3) = 3w + 22\]
Select correct first step:
\( 3(4w - 3) = 3w + 22 \)
\( 5 - 8w + 6 = 3w + 22 \)
\( 5 - 8w - 6 = 3w + 22 \)
\( 5 - 8w - 3 = 3w + 22 \)
MY WORKSPACE
QUESTION 3 Solve the equation:
\[12 - (5y - 8) = -2y + 5\]
Select correct first step:
\( 12 - 5y - 8 = -2y + 5 \)
\( 7 - 5y = -2y + 5 \)
\( 12 + 5y - 8 = -2y + 5 \)
\( 12 - 5y + 8 = -2y + 5 \)
MY WORKSPACE
QUESTION 4 Solve the equation:
\[-4(3 - 2m) - 5m = m - 24\]
Select correct first step:
\( -12 + 8m - 5m = m - 24 \)
\( -12 - 8m - 5m = m - 24 \)
\( -12 + 2m - 5m = m - 24 \)
\( -12 - 2m - 5m = m - 24 \)
MY WORKSPACE
Pro-Tip: Multiplying a negative number by a negative number results in a positive. Don't fall for the trap!
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Sign Trap Warmup Answer Key
SIGN TRAP WARMUP
ANSWER KEY
Teacher Reference & Exemplar Guide
Teacher Edition / Full Solutions
Key Misconceptions: Highlighted correct answers are bordered in green. Worked steps feature specific distributive color highlights.
QUESTION 1 Equation:
\[-3(2x - 5) + 4x = 29\]
Select correct first step:
\( -6x - 5 + 4x = 29 \)
\( -6x - 15 + 4x = 29 \)
\( -6x + 15 + 4x = 29 \)
\( -6x + 15 - 12x = 29 \)
EXTREMPLAR SOLUTION
\( -6x + 15 + 4x = 29 \) (Distribute \( -3 \))
\( -2x + 15 = 29 \) (Combine terms)
\( -2x = 14 \) (Subtract 15)
\( x = -7 \) (Divide by \( -2 \))
QUESTION 2 Equation:
\[5 - 2(4w - 3) = 3w + 22\]
Select correct first step:
\( 3(4w - 3) = 3w + 22 \)
\( 5 - 8w + 6 = 3w + 22 \)
\( 5 - 8w - 6 = 3w + 22 \)
\( 5 - 8w - 3 = 3w + 22 \)
EXTREMPLAR SOLUTION
\( 5 - 8w + 6 = 3w + 22 \) (Distribute \( -2 \))
\( 11 - 8w = 3w + 22 \) (Combine const)
\( 11 = 11w + 22 \) (Add \( 8w \))
\( -11 = 11w \) (Subtract 22)
\( w = -1 \) (Divide by 11)
QUESTION 3 Equation:
\[12 - (5y - 8) = -2y + 5\]
Select correct first step:
\( 12 - 5y - 8 = -2y + 5 \)
\( 7 - 5y = -2y + 5 \)
\( 12 + 5y - 8 = -2y + 5 \)
\( 12 - 5y + 8 = -2y + 5 \)
EXTREMPLAR SOLUTION
\( 12 - 5y + 8 = -2y + 5 \) (Distribute \( -1 \))
\( 20 - 5y = -2y + 5 \) (Combine const)
\( 20 = 3y + 5 \) (Add \( 5y \))
\( 15 = 3y \) (Subtract 5)
\( y = 5 \) (Divide by 3)
QUESTION 4 Equation:
\[-4(3 - 2m) - 5m = m - 24\]
Select correct first step:
\( -12 + 8m - 5m = m - 24 \)
\( -12 - 8m - 5m = m - 24 \)
\( -12 + 2m - 5m = m - 24 \)
\( -12 - 2m - 5m = m - 24 \)
EXTREMPLAR SOLUTION
\( -12 + 8m - 5m = m - 24 \) (Distribute \( -4 \))
\( -12 + 3m = m - 24 \) (Combine terms)
\( -12 + 2m = -24 \) (Subtract \( m \))
\( 2m = -12 \) (Add 12)
\( m = -6 \) (Divide by 2)
Pedagogical Strategy: Use these common misconceptions as classroom discussion prompts to address why they are mathematical traps.
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