One- and Two-Step Equations
Practice isolating variables with inverse operations and checking your solutions.
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Questions Covered in This Set
12 cards to master
What is an equation?
A statement that two expressions are equal, such as x + 7 = 12.
What does it mean to 'solve' an equation?
To find every value of the variable that makes the statement true.
Name the two pairs of inverse operations.
Addition ↔ Subtraction, and Multiplication ↔ Division.
Why is the equal sign like a balance scale?
Whatever you do to one side you must do to the other, or the equation is no longer true.
Solve: 6y = 42
Divide both sides by 6: y = 7. Check: 6(7) = 42 ✓
Solve: x/5 = 3
Multiply both sides by 5: x = 15. Check: 15/5 = 3 ✓
In a two-step equation, which operation do you undo first?
Undo addition/subtraction first, then multiplication/division — reverse order of operations.
Solve: 3x + 5 = 20
Subtract 5 → 3x = 15; divide by 3 → x = 5. Check: 3(5)+5 = 20 ✓
Solve: -2x + 9 = 1
Subtract 9 → -2x = -8; divide by -2 → x = 4. The sign travels with the coefficient.
Solve: 7 - x = 10
Subtract 7 → -x = 3; multiply by -1 → x = -3.
Taxi: $3 flat fee plus $2 per mile, total $17. How many miles?
2m + 3 = 17 → 2m = 14 → m = 7 miles.
How do you solve (2/3)t = 8?
Multiply both sides by the reciprocal 3/2: t = 12.
