Variable Escape Exit Ticket
Quick Assessment
VARIABLE ESCAPE
Topic: Multi-Step Equations with Variables on Both Sides
Name:
Date:
Period:
Directions
Solve each equation below. Show your complete step-by-step algebraic work in the designated workspace. Write your final simplified value in the solution box on the bottom right of each section.
1
Solve for \(y\)
\[6(y + 15.5) = 11y - 32\]
Distribute first, then combine like terms.
Algebraic Workspace
y =
2
Solve for \(p\)
\[5(p + 12.4) = 9p - 10\]
Isolate variables on one side of the equation.
Algebraic Workspace
p =
3
Solve for \(w\)
\[8(w + 10.25) = 13w - 18\]
Divide or multiply to isolate the final variable.
Algebraic Workspace
w =
Standard Focus: CCSS.MATH.CONTENT.8.EE.C.7.B
Distributed correctly Consolidated constants Isolated variable
Variable Escape Answer Key
Teacher Resource
VARIABLE ESCAPE
★ Answer Key & Solved Steps ★
Subject: Algebra 1 / Grade 8
Focus: Linear Equations
Pacing: 5-10 Minute Formative
Grading & Solutions Guide
This key outlines the step-by-step deductive methods to isolate the variables. Look for correct distribution of coefficients, isolation of variables, and correct arithmetic steps.
1
Solve for \(y\)
\[6(y + 15.5) = 11y - 32\]
Distribute first, then combine like terms.
Solved Steps
-
Distribute the 6: \(6y + 93 = 11y - 32\)
-
Subtract \(6y\) from both sides: \(93 = 5y - 32\)
-
Add 32 to both sides: \(125 = 5y\)
-
Divide by 5: \(y = 25\)
y = 25
2
Solve for \(p\)
\[5(p + 12.4) = 9p - 10\]
Isolate variables on one side of the equation.
Solved Steps
-
Distribute the 5: \(5p + 62 = 9p - 10\)
-
Subtract \(5p\) from both sides: \(62 = 4p - 10\)
-
Add 10 to both sides: \(72 = 4p\)
-
Divide by 4: \(p = 18\)
p = 18
3
Solve for \(w\)
\[8(w + 10.25) = 13w - 18\]
Divide or multiply to isolate the final variable.
Solved Steps
-
Distribute the 8: \(8w + 82 = 13w - 18\)
-
Subtract \(8w\) from both sides: \(82 = 5w - 18\)
-
Add 18 to both sides: \(100 = 5w\)
-
Divide by 5: \(w = 20\)
w = 20
Standard Focus: CCSS.MATH.CONTENT.8.EE.C.7.B
Distributed correctly Consolidated constants Isolated variable
