Distribution Showdown Worksheet + TOP_LEFT
PAGE_01 +
+ MATH_ALGEBRA_1
DIST_SHOWDOWN +
ALGEBRA 1 TRAINING MANUAL
DISTRIBUTION SHOWDOWN
NAME:
DATE:
PERIOD:
Your Mission
Master the power of algebraic distribution! In this showdown, you will unlock terms by distributing the factor outside the parentheses to everything inside. Watch out for negative values—they change the sign of every term they touch!
PHASE 1
Simplifying Expressions
WORKED EXAMPLE & METHODOLOGY Simplify: \(-3(2x - 5) + 4x\)
Step 1: Distribute
Multiply the external factor \(-3\) to both inner terms.
\((-3 \cdot 2x) + (-3 \cdot -5)\)
Step 2: Sign Watch
Be careful! A negative times a negative is positive.
\(-6x + 15 + 4x\)
Step 3: Combine
Group and combine all similar algebraic terms.
\(-2x + 15\)
INDEPENDENT PRACTICE
SHOW ALL STEPS FOR CREDIT
PROBLEM 01 Simplify
\( 4(x + 6) - 2(3x - 1) \)
PROBLEM 02 Simplify
\( 5(3 - 2a) - (4a - 1) \)
PROBLEM 03 Simplify
\( -2(4k - 3) - 3(2k + 1) \)
PROBLEM 04 Simplify
\( -6(x - 2) + 2(3x - 4) \)
PROBLEM 05 Simplify
\( -(5 - 2m) - 4(2m + 3) \)
PROBLEM 06 Simplify
\( 3(3y - 2) - 5(y + 4) \)
DISTRIBUTION SHOWDOWN • STUDENT WORKPASS PAGE 1 OF 2
+ TOP_LEFT
PAGE_02 +
+ MATH_ALGEBRA_1
DIST_SHOWDOWN +
ALGEBRA 1 TRAINING MANUAL
THE SHOWDOWN: EQUATIONS
DOUBLE DISTRIBUTION
PHASE 2
Solving Multi-Step Equations
THE SOLVING BLUEPRINT Solve: \(3(2x - 4) = 2(x + 8)\)
1. Distribute
\(6x - 12 = 2x + 16\)
Remove all parenthesis first.
2. Shift Variable
\(4x - 12 = 16\)
Subtract \(2x\) from both sides.
3. Isolate Term
\(4x = 28\)
Add \(12\) to both sides.
4. Solve & Check
\(x = 7\)
Divide both sides by \(4\).
PRACTICE MISSIONS
INTEGERS ONLY • WORK VERTICALLY
MISSION 01 Solve for \(x\)
\( 4(x - 3) = 2(x + 6) \)
MISSION 02 Solve for \(y\)
\( -3(2y + 4) = 3(y - 7) \)
MISSION 03 Solve for \(a\)
\( 5(a - 2) = -2(a + 12) \)
MISSION 04 Solve for \(k\)
\( 2(3k - 1) = 5(k + 2) - 4 \)
MISSION 05 Solve for \(w\)
\( -2(3w - 5) = 4(w - 1) - 6 \)
MISSION 06 Solve for \(x\)
\( -3(x + 4) = -(5x + 2) \)
DISTRIBUTION SHOWDOWN • STUDENT WORKPASS PAGE 2 OF 2
Distribution Showdown Answer Key + TEACHER_KEY
PAGE_01 +
+ MATH_ALGEBRA_1
DIST_SHOWDOWN_KEY +
TEACHER ANSWER KEY • REFERENCE ONLY
DISTRIBUTION SHOWDOWN
NAME: ANSWER KEY
DATE: CLASS USE
PERIOD: 1 - 7
Teacher Reference Guide
This document contains detailed step-by-step worked solutions for the algebraic distribution sequence. Final simplified answers and variable values are highlighted in bold red.
PHASE 1
Simplifying Expressions (Solutions)
WORKED EXAMPLE & METHODOLOGY Simplify: \(-3(2x - 5) + 4x\)
Step 1: Distribute
Multiply the external factor \(-3\) to both inner terms.
\((-3 \cdot 2x) + (-3 \cdot -5)\)
Step 2: Sign Watch
Be careful! A negative times a negative is positive.
\(-6x + 15 + 4x\)
Step 3: Combine
Group and combine all similar algebraic terms.
\(-2x + 15\)
KEY SHEET (SOLVED)
DETAILED INTERMEDIATE STEPS SHOWN
PROBLEM 01 Answer Key
\( 4(x + 6) - 2(3x - 1) \)
\(\rightarrow 4x + 24 - 6x + 2\)
Final: \(-2x + 26\)
PROBLEM 02 Answer Key
\( 5(3 - 2a) - (4a - 1) \)
\(\rightarrow 15 - 10a - 4a + 1\)
Final: \(-14a + 16\)
PROBLEM 03 Answer Key
\( -2(4k - 3) - 3(2k + 1) \)
\(\rightarrow -8k + 6 - 6k - 3\)
Final: \(-14k + 3\)
PROBLEM 04 Answer Key
\( -6(x - 2) + 2(3x - 4) \)
\(\rightarrow -6x + 12 + 6x - 8\)
Final: \(4\)
PROBLEM 05 Answer Key
\( -(5 - 2m) - 4(2m + 3) \)
\(\rightarrow -5 + 2m - 8m - 12\)
Final: \(-6m - 17\)
PROBLEM 06 Answer Key
\( 3(3y - 2) - 5(y + 4) \)
\(\rightarrow 9y - 6 - 5y - 20\)
Final: \(4y - 26\)
DISTRIBUTION SHOWDOWN • TEACHER ANSWER PASS PAGE 1 OF 2
+ TEACHER_KEY
PAGE_02 +
+ MATH_ALGEBRA_1
DIST_SHOWDOWN_KEY +
TEACHER ANSWER KEY • REFERENCE ONLY
THE SHOWDOWN: EQUATIONS
DOUBLE DISTRIBUTION
PHASE 2
Solving Multi-Step Equations
THE SOLVING BLUEPRINT Solve: \(3(2x - 4) = 2(x + 8)\)
1. Distribute
\(6x - 12 = 2x + 16\)
Remove all parenthesis first.
Distribution Showdown Slides MISSION BRIEFING UNIT 02 // ALGEBRA 1
PHASE 01: SIMPLIFYING & SOLVING
DISTRIBUTION
SHOWDOWN
Unlock algebraic expressions and solve equations with standard and double distribution.
Tactical Math Series
LAUNCH PRESENTATION • SLIDE 1
TACTICAL RULE THE METHOD
The Rule of the Gate
THE CORE IDENTITY
\(a(b + c) = ab + ac\)
Factor Outside → Multiplies ALL Inside
Knock Down the Walls
Distribution gets rid of parentheses, letting you group free terms.
Watch the Signs!
If the factor outside is negative, it reverses the sign of every term inside.
DISTRIBUTION RULES SLIDE 2
GUIDED EXERCISE SIMPLIFYING DEMO
Simplifying with Distribution
Simplify: \(-3(2x - 5) + 4x\)
STEP 1
Distribute \(-3\)
Multiply the outer term into both inner terms.
\((-3 \cdot 2x) + (-3 \cdot -5)\)
STEP 2
Sign Watch
Simplify products. Negative times negative is positive!
\(-6x + 15 + 4x\)
STEP 3
Combine Terms
Group like terms together to find the final result.
\(-2x + 15\)
PHASE 1 WORKED EXAMPLE SLIDE 3
TACTICAL PLAN DOUBLE DISTRIBUTION
Double Distribution Rules
When a variable is trapped behind parentheses on both sides of an equation:
1
Clear both sides
Perform standard distribution on both sides of the equals sign.
2
Group the terms
Combine any like terms sitting on the same side of the equation.
3
Collect variables
Use inverse operations to shift variables to one side.
4
Isolate & solve
Undo operations to isolate the variable. Verify with checks.
EQUATION SEQUENCE SLIDE 4
TACTICAL DEMO EQUATIONS IN ACTION
Solving: \(3(2x - 4) = 2(x + 8)\)
1 Distribute both sides: \(6x - 12 = 2x + 16\)
2 Subtract \(2x\) from both sides: \(4x - 12 = 16\)
3 Add \(12\) to both sides: \(4x = 28\)
4 Divide by \(4\): \(x = 7\)
Mission Pro-Tip
Always subtract the smaller coefficient variable first (shifting \(2x\) instead of \(6x\)). This guarantees you work with positive variables whenever possible and simplifies arithmetic!
