Equation Equilibrium Worksheet
Equation Equilibrium
Two-Step Linear Equations • Part 1
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Directions: Use inverse operations to isolate each variable in two steps. Keep equations balanced by performing each operation on both sides.
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1 \(3x + 7 = 25\) Mult / Add
2 \(5m - 8 = 27\) Mult / Sub
3 \(\dfrac{p}{4} + 6 = 11\) Div / Add
4 \(\dfrac{k}{3} - 5 = 4\) Div / Sub
5 \(9 + 4y = 41\) Add / Mult
6 \(6w - 15 = 21\) Mult / Sub
Algebra Fundamentals • Two-Step Equations Inverse addition/subtraction before multiplication/division Page 1 of 4
Equation Equilibrium
Two-Step Linear Equations • Part 2
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Practice Check: Keep operations balanced on both sides of the equal sign.
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7 \(\dfrac{n}{6} + 8 = 15\) Div / Add
8 \(34 = 7a - 8\) Mult / Sub
9 \(\dfrac{h}{5} - 7 = 3\) Div / Sub
10 \(8b + 19 = 75\) Mult / Add
11 \(12 + \dfrac{t}{2} = 21\) Add / Div
12 \(9c - 16 = 56\) Mult / Sub
Algebra Fundamentals • Two-Step Equations Inverse pairs: addition & subtraction, multiplication & division Page 2 of 4
Equation Equilibrium
Two-Step Linear Equations • Part 3
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Multi-Step Routine: First isolate the variable term, then multiply or divide to solve for the variable.
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13 \(4a + 15 = 47\) Mult / Add
14 \(\dfrac{u}{7} - 3 = 5\) Div / Sub
15 \(8r - 23 = 41\) Mult / Sub
16 \(\dfrac{z}{4} + 9 = 16\) Div / Add
17 \(29 = 3d - 7\) Mult / Sub
18 \(14 + \dfrac{v}{5} = 22\) Add / Div
Algebra Fundamentals • Two-Step Equations Maintain equivalence by executing the same operation on each side Page 3 of 4
Equation Equilibrium
Two-Step Linear Equations • Part 4
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Final Set: Solve Problems 19–22 below, then choose any two equations on the worksheet to check by substitution!
Final Practice
19 \(7g + 18 = 67\) Mult / Add
20 \(\dfrac{q}{8} - 6 = 2\) Div / Sub
21 \(11s - 25 = 52\) Mult / Sub
22 \(19 = \dfrac{w}{3} + 11\) Div / Add
Solution Verification Station (Check by Substitution)
Substitute your solution into the original equation
Check Equation # _______ Left Side = Right Side?
Check Equation # _______ Left Side = Right Side?
Algebra Fundamentals • Two-Step Equations Self-check mastery: A solution makes the original equality true Page 4 of 4
