Distributive Duels Practice Worksheet
TEKS A.5(A) Practice
DISTRIBUTIVE DUELS
Solving Multi-Step Equations with Variables on Both Sides
Name: ___________________
Date: ________
Period: _____
Level 1: Single Distribution (Integers)
Goal: Distribute the coefficient on one side of the equation first, then gather variables on one side and constants on the other.
Problem 1
\(2(3x - 4) = 4x + 10\)
Distribute the 2:
( 2 · 3x ) - ( 2 · 4 ) = 4x + 10
Show algebraic steps here
Final Solution
x = ______
Problem 2
\(5(2y + 3) = 7y - 3\)
Distribute the 5:
( 5 · 2y ) + ( 5 · 3 ) = 7y - 3
Show algebraic steps here
Final Solution
y = ______
Problem 3
\(3(-4w + 5) = -9w + 3\)
Distribute with negative term:
( 3 · -4w ) + ( 3 · 5 ) = -9w + 3
Show algebraic steps here
Final Solution
w = ______
Problem 4
\(-4(2a - 3) = -5a - 3\)
Distributing a Negative:
( -4 · 2a ) - ( -4 · 3 ) = -5a - 3
Show algebraic steps here
Final Solution
a = ______
Unit: Linear Equations & Inequalities Page 1 of 4
L2
DISTRIBUTIVE DUELS WORKBOOK
TEKS A.5(A)
Level 2: Double Distribution (Integers)
Goal: Distribute on both sides of the equation. Watch your signs closely when distributing negative factors!
Problem 5
\(-2(x - 5) = 3(x + 5)\)
Left Side Right Side
-2x + 10 = 3x + 15
Show algebraic steps here
Final Solution
x = ______
Problem 6
\(-3(2y - 4) = -(y + 3)\)
Distribute -3 Distribute Negative
-6y + 12 = -y - 3
Show algebraic steps here
Final Solution
y = ______
Problem 7
\(4(w - 2) = -2(w - 8)\)
Distribute 4 Distribute -2
4w - 8 = -2w + 16
Show algebraic steps here
Final Solution
w = ______
Problem 8
\(-5(a + 2) = -2(2a + 7)\)
Distribute -5 Distribute -2
-5a - 10 = -4a - 14
Show algebraic steps here
Final Solution
a = ______
Unit: Linear Equations & Inequalities Page 2 of 4
L3
DISTRIBUTIVE DUELS WORKBOOK
TEKS A.5(A)
Level 3: Single Distribution (Decimals)
Goal: Distribute thoroughly, being mindful of place value when multiplying decimal constants and coefficients!
Problem 9
\(2(x + 4.5) = 5x - 6\)
Decimal Multiplication:
( 2 · x ) + ( 2 · 4.5 ) = 5x - 6
Show algebraic steps here
Final Solution
x = ______
Problem 10
\(4(y - 2.25) = 2.5y + 6\)
Decimal Multiplication:
( 4 · y ) - ( 4 · 2.25 ) = 2.5y + 6
Show algebraic steps here
Final Solution
y = ______
Problem 11
\(5(0.6w + 2) = 2w + 16\)
Distribute across 0.6w:
( 5 · 0.6w ) + ( 5 · 2 ) = 2w + 16
Show algebraic steps here
Final Solution
w = ______
Problem 12
\(-3(a - 1.5) = 1.5a - 9\)
Distribute Negative Factor:
( -3 · a ) - ( -3 · 1.5 ) = 1.5a - 9
Show algebraic steps here
Final Solution
a = ______
Unit: Linear Equations & Inequalities Page 3 of 4
L4
DISTRIBUTIVE DUELS WORKBOOK
TEKS A.5(A)
Level 4: Double Distribution (Decimals / Fractions)
Goal: Conquer the ultimate challenge! Carefully expand multiple distribution blocks with combinations of positive/negative decimals.
Problem 13
\(2(1.5x - 4) = x - 0.5(12 - 2x)\)
Multi-Step Roadmap:
Distribute LHS
Distribute RHS
Combine Like Terms on RHS
Show algebraic steps here
Final Solution
x = ______
Problem 14
\(4(0.5y - 3) = y - 0.25(16 - 8y)\)
Multi-Step Roadmap:
Distribute LHS
Distribute RHS
Combine Like Terms on RHS
Show algebraic steps here
Final Solution
y = ______
Problem 15
\(5(0.8w - 2) = w - 0.5(8 - 4w)\)
Multi-Step Roadmap:
Distribute LHS
Distribute RHS
Combine Like Terms on RHS
Show algebraic steps here
Final Solution
w = ______
Problem 16
\(6(0.5a + 1.5) = a - 0.2(10 - 15a)\)
Multi-Step Roadmap:
Distribute LHS
Distribute RHS
Combine Like Terms on RHS
Show algebraic steps here
Final Solution
a = ______
Unit: Linear Equations & Inequalities Page 4 of 4
Distributive Duels Partner Match
Cooperative Learning Activity
PARTNER MATCH
Solving Equations • Self-Checking Collaboration
PARTNER A: ______________
Date: ________
My Partner's Name: __________________
Directions: Solve each equation in your workspace. When you and your partner are both finished, compare your final answers for each problem number. Even though your equations are different, your answers should be identical! If your answers don't match, work together to identify and correct any distribution or arithmetic mistakes.
Problem 1 Level 1
\(3(2x - 5) = x + 5\)
Show work here
x =
Problem 2 Level 1
\(4(3x + 10) = 2x + 10\)
Show work here
x =
Problem 3 Level 2
\(-3(x - 4) = 2(x + 1)\)
Show work here
x =
Problem 4 Level 2
\(-2(2x - 3) = -(x - 12)\)
Show work here
x =
Problem 5 Level 3
\(2(x + 3.5) = 4x - 3\)
Show work here
x =
Problem 6 Level 3
\(4(x - 1.5) = 2.5x + 3\)
Show work here
x =
Problem 7 Level 4
\(2(1.5x - 1) = x - 0.5(10 - 6x)\)
Show work here
x =
Problem 8 Level 4
\(4(0.5x - 2) = x - 0.5(12 - 4x)\)
Show work here
x =
Collaborative Partner Playbook Partner A Side
Cooperative Learning Activity
PARTNER MATCH
Solving Equations • Self-Checking Collaboration
PARTNER B: ______________
Date: ________
My Partner's Name: __________________
Directions: Solve each equation in your workspace. When you and your partner are both finished, compare your final answers for each problem number. Even though your equations are different, your answers should be identical! If your answers don't match, work together to identify and correct any distribution or arithmetic mistakes.
Problem 1 Level 1
\(2(x + 3) = 5x - 6\)
Show work here
x =
Problem 2 Level 1
\(-2(x - 4) = -5x - 1\)
Show work here
x =
Problem 3 Level 2
\(4(x - 5) = -2(x + 4)\)
Show work here
