Equation Builders Worksheet
Algebra 1 Practice Linear Equations
EQUATION BUILDERS
Combining Like Terms & Multi-Step Equations
Name:
Date:
Period:
1
Part 1: Simplify Expressions
Combine like terms. Write answers in simplest form.
- \( 4x + 7 + 2x - 3 \)
Ans:
- \( 5y - 8 - 9y + 12 \)
Ans:
- \( 2.4a + 1.8 + 3.1a - 0.5 \)
Ans:
- \( 7k - 3.2 - 4k + 1.6 \)
Ans:
- \( \frac{3}{5}m + 4 + \frac{1}{5}m - 2 \)
Ans:
- \( \frac{1}{2}w + 6 + \frac{1}{4}w - 5 \)
Ans:
2
Part 2: Solve Equations with Like Terms
Combine like terms on one side, then isolate the variable.
- \( 3x + 4x = 21 \)
Show work:
\( x = \)
- \( 5y - 2y + 8 = 20 \)
Show work:
\( y = \)
- \( 8m - 3m - 7 = 18 \)
Show work:
\( m = \)
- \( 1.5p + 2.5p = 16 \)
Show work:
\( p = \)
- \( 6n - 2n + 4.5 = 16.5 \)
Show work:
\( n = \)
- \( \frac{2}{3}w + \frac{1}{3}w + 4 = 11 \)
Show work:
\( w = \)
Equation Builders • Algebra 1 Practice Page 1 of 2
EQUATION BUILDERS | Multi-Step & Both Sides
Student:
3
Part 3: Variables on Both Sides
Collect variables on one side and constants on the other.
- \( 5x + 3 = 2x + 15 \)
Show work:
\( x = \)
- \( 7y - 4 = 4y + 11 \)
Show work:
\( y = \)
- \( 9a - 12 = 3a + 6 \)
Show work:
\( a = \)
- \( 4.5m + 2 = 2.5m + 10 \)
Show work:
\( m = \)
- \( 8k + 5 = 11k - 7 \)
Show work:
\( k = \)
- \( \frac{3}{4}t + 2 = \frac{1}{4}t + 5 \)
Show work:
\( t = \)
4
Part 4: Multi-Step Equations
Distribute, combine like terms, and solve.
- \( 2(x + 4) + 3x = 23 \)
Show work:
\( x = \)
- \( 4(y - 2) - y = 13 \)
Show work:
\( y = \)
- \( 3(2m + 1) = 4m + 11 \)
Show work:
\( m = \)
- \( 2(2p - 1) + 5 = 15 \)
Show work:
\( p = \)
- \( 0.5(4n + 6) = 11 \)
Show work:
\( n = \)
- \( \frac{1}{3}(6w - 9) + 4 = 9 \)
Show work:
\( w = \)
Equation Builders • Algebra 1 Practice Page 2 of 2
Equation Builders Answer Key
Teacher Resource Answer Key & Solutions
EQUATION BUILDERS
Combining Like Terms & Multi-Step Equations
Master Key Full Step-by-Step Solutions
1
Part 1: Simplify Expressions
6 Problems
- \( 4x + 7 + 2x - 3 \)
\( (4x + 2x) + (7 - 3) \)
Ans: \( 6x + 4 \)
- \( 5y - 8 - 9y + 12 \)
\( (5y - 9y) + (-8 + 12) \)
Ans: \( -4y + 4 \)
- \( 2.4a + 1.8 + 3.1a - 0.5 \)
\( (2.4a + 3.1a) + (1.8 - 0.5) \)
Ans: \( 5.5a + 1.3 \)
- \( 7k - 3.2 - 4k + 1.6 \)
\( (7k - 4k) + (-3.2 + 1.6) \)
Ans: \( 3k - 1.6 \)
- \( \frac{3}{5}m + 4 + \frac{1}{5}m - 2 \)
\( \left(\frac{3}{5} + \frac{1}{5}\right)m + (4 - 2) \)
Ans: \( \frac{4}{5}m + 2 \)
- \( \frac{1}{2}w + 6 + \frac{1}{4}w - 5 \)
\( \left(\frac{2}{4} + \frac{1}{4}\right)w + (6 - 5) \)
Ans: \( \frac{3}{4}w + 1 \)
2
Part 2: Solve Equations with Like Terms
6 Problems
- \( 3x + 4x = 21 \)
\( 7x = 21 \)
\( x = 21 \div 7 \)
\( x = 3 \)
- \( 5y - 2y + 8 = 20 \)
\( 3y + 8 = 20 \implies 3y = 12 \)
\( y = 12 \div 3 \)
\( y = 4 \)
- \( 8m - 3m - 7 = 18 \)
\( 5m - 7 = 18 \implies 5m = 25 \)
\( m = 25 \div 5 \)
\( m = 5 \)
- \( 1.5p + 2.5p = 16 \)
\( 4p = 16 \)
\( p = 16 \div 4 \)
\( p = 4 \)
- \( 6n - 2n + 4.5 = 16.5 \)
\( 4n + 4.5 = 16.5 \implies 4n = 12 \)
\( n = 12 \div 4 \)
\( n = 3 \)
- \( \frac{2}{3}w + \frac{1}{3}w + 4 = 11 \)
\( \frac{3}{3}w + 4 = 11 \implies 1w + 4 = 11 \)
\( w = 11 - 4 \)
\( w = 7 \)
Equation Builders • Teacher Answer Key Page 1 of 2
EQUATION BUILDERS | Answer Key • Page 2
Parts 3 & 4 Solutions
3
Part 3: Variables on Both Sides
6 Problems
- \( 5x + 3 = 2x + 15 \)