Equation Crunch Exit Ticket
Warm-Up / Exit Ticket
Equation Crunch
Name:
Date:
Period:
Mastering multi-step equations of the form \( a(b - cv) + d = e \). Be sure to distribute, combine like terms first, and show every step of your work!
Concept Blueprint: Distribute & Combine Like Terms
Worked Example
\( 8(2 - 6v) + 19 = -61 \)
\( \rightarrow 16 - 48v + 19 = -61 \)
\( \rightarrow 35 - 48v = -61 \)
\( \rightarrow -48v = -96 \)
\( \rightarrow v = 2 \)
1
Distribute: Multiply \(8\) by both \(2\) and \(-6v\).
2
Combine Like Terms: Add the constants \(16\) and \(19\).
3
Isolate Variable: Subtract \(35\), then divide by \(-48\).
Your Turn: Practice Problems
1 Solve for \( x \): Score: ______ / 5
\( 6(4 - 5x) + 15 = -51 \)
Show every step (distribute, combine, solve) \( x = \) _________
2 Solve for \( y \): Score: ______ / 5
\( 5(3 - 4y) + 22 = -43 \)
Show every step (distribute, combine, solve) \( y = \) _________
3 Solve for \( v \): Score: ______ / 5
\( 7(5 - 3v) + 12 = -37 \)
Show every step (distribute, combine, solve) \( v = \) _________
Self-Check: Did you double check your arithmetic with substitution?
Distribute: ▢ Combine: ▢ Solve: ▢
Equation Crunch Teacher Key
Teacher Reference
Equation Crunch Answer Key
Class:
Algebra 1 / Math 8
Standard:
CCSS.MATH.8.EE.C.7.B
Focus:
Like Terms & Dist.
Full algebraic proofs and grading checkpoints for multi-step equations of the form \( a(b - cv) + d = e \).
Concept Blueprint: Distribute & Combine Like Terms
Worked Example
\( 8(2 - 6v) + 19 = -61 \)
\( \rightarrow 16 - 48v + 19 = -61 \)
\( \rightarrow 35 - 48v = -61 \)
\( \rightarrow -48v = -96 \)
\( \rightarrow v = 2 \)
1
Distribute: Multiply \(8\) by both \(2\) and \(-6v\).
2
Combine Like Terms: Add the constants \(16\) and \(19\).
3
Isolate Variable: Subtract \(35\), then divide by \(-48\).
Checkpoints & Complete Solutions
1 Solve for \( x \): Checkpoint Reference
\( 6(4 - 5x) + 15 = -51 \)
Step 1 (Distribute): \( 24 - 30x + 15 = -51 \) 1 pt
Step 2 (Combine Constants): \( 39 - 30x = -51 \) 2 pts
Step 3 (Isolate): \( -30x = -90 \) 1 pt
Verification: \( 6(4-15)+15 = 6(-11)+15 = -51 \) (OK) \( x = 3 \) (1 pt)
2 Solve for \( y \): Checkpoint Reference
\( 5(3 - 4y) + 22 = -43 \)
Step 1 (Distribute): \( 15 - 20y + 22 = -43 \) 1 pt
Step 2 (Combine Constants): \( 37 - 20y = -43 \) 2 pts
Step 3 (Isolate): \( -20y = -80 \) 1 pt
Verification: \( 5(3-16)+22 = 5(-13)+22 = -43 \) (OK) \( y = 4 \) (1 pt)
3 Solve for \( v \): Checkpoint Reference
\( 7(5 - 3v) + 12 = -37 \)
Step 1 (Distribute): \( 35 - 21v + 12 = -37 \) 1 pt
Step 2 (Combine Constants): \( 47 - 21v = -37 \) 2 pts
Step 3 (Isolate): \( -21v = -84 \) 1 pt
Verification: \( 7(5-12)+12 = 7(-7)+12 = -37 \) (OK) \( v = 4 \) (1 pt)
Grading Note: Award partial credit according to step markers shown in red boxes.
Distribute: 1pt Combine: 2pt Solve: 2pt
