Two-step equations
Solve equations that require two inverse operations, including equations with negatives, fractions, and variables on both sides.
Worked examples
Solving a two-step equation
Straightforward
Problem
Solve .
1
Identify what has been done to , in order.
has been multiplied by 5, then 3 has been subtracted.
2
Undo the operations in reverse order. First, undo the subtraction by adding 3 to both sides.
3
Undo the multiplication by dividing both sides by 5.
4
Check by substituting back into the original equation.
Answer
Two-step equation with a negative solution
Moderate
Problem
Solve .
1
Subtract 5 from both sides to undo the addition.
2
Divide both sides by 2 to undo the multiplication.
3
Check by substituting back into the original equation.
Answer
Equation with variables on both sides
Challenging
Problem
Solve .
1
Collect the terms on one side by subtracting from both sides.
2
Add 3 to both sides to isolate the term.
3
Divide both sides by 3.
4
Check by substituting into both sides of the original equation.
Left side:
Right side: \checkmark
Right side: \checkmark
Answer
Practise
Q1·Straightforward
Solve .
Explanation
Subtract 3 from both sides:
Divide both sides by 2:
Divide both sides by 2:
Q2·Straightforward
Solve .
Explanation
Subtract 1 from both sides:
Divide both sides by 3:
Divide both sides by 3:
Q3·Straightforward
Solve .
Explanation
Add 5 to both sides:
Divide both sides by 4:
Divide both sides by 4:
Q4·Straightforward
Solve .
Explanation
Subtract 2 from both sides:
Divide both sides by 6:
Divide both sides by 6:
Q5·Moderate
Solve .
Explanation
Add 7 to both sides:
Divide both sides by 3:
Divide both sides by 3:
Q6·Moderate
Solve .
Explanation
Subtract 4 from both sides:
Multiply both sides by 3:
Multiply both sides by 3:
Q7·Moderate
Solve .
Explanation
Subtract 9 from both sides:
Divide both sides by 2:
Divide both sides by 2:
Q8·Moderate
Solve .
Explanation
Add 2 to both sides:
Multiply both sides by 4:
Multiply both sides by 4:
Q9·Challenging
Solve .
Explanation
Subtract from both sides:
Subtract 2 from both sides:
Divide both sides by 2:
Subtract 2 from both sides:
Divide both sides by 2:
Q10·Challenging
Solve .
Explanation
Subtract from both sides:
Add 3 to both sides:
Divide both sides by 2:
Add 3 to both sides:
Divide both sides by 2:
Q11·Challenging
Solve .
Explanation
Subtract from both sides:
Add 8 to both sides:
Divide both sides by 3:
Add 8 to both sides:
Divide both sides by 3:
Q12·Challenging
Solve .
Explanation
Subtract from both sides:
Add 4 to both sides:
Divide both sides by 3:
Add 4 to both sides:
Divide both sides by 3: