Solving Two-Step Equations
Use inverse operations to find the unknown value
Solving Two-Step Equations
Use inverse operations to find the unknown value
Math - Grade 6-8
- 1
Solve for x: 3x + 5 = 20.
Undo the addition first, then undo the multiplication.
Subtract 5 from both sides to get 3x = 15. Divide both sides by 3, so x = 5. - 2
Solve for y: 4y - 7 = 17.
Add 7 to both sides to get 4y = 24. Divide both sides by 4, so y = 6. - 3
Solve for n: n/5 + 9 = 14.
The opposite of dividing by 5 is multiplying by 5.
Subtract 9 from both sides to get n/5 = 5. Multiply both sides by 5, so n = 25. - 4
Solve for a: 2a + 11 = 31.
Subtract 11 from both sides to get 2a = 20. Divide both sides by 2, so a = 10. - 5
Solve for p: 6p - 8 = 28.
Keep the equation balanced by doing the same operation to both sides.
Add 8 to both sides to get 6p = 36. Divide both sides by 6, so p = 6. - 6
Solve for m: m/3 - 4 = 10.
Add 4 to both sides to get m/3 = 14. Multiply both sides by 3, so m = 42. - 7
Solve for z: 5z + 2 = -18.
A positive number divided into a negative number gives a negative answer.
Subtract 2 from both sides to get 5z = -20. Divide both sides by 5, so z = -4. - 8
Solve for t: -2t + 6 = 16.
Subtract 6 from both sides to get -2t = 10. Divide both sides by -2, so t = -5. - 9
Solve for r: 7r - 3 = 39.
Undo subtraction before undoing multiplication.
Add 3 to both sides to get 7r = 42. Divide both sides by 7, so r = 6. - 10
Solve for k: k/2 + 6 = 13.5.
Subtract 6 from both sides to get k/2 = 7.5. Multiply both sides by 2, so k = 15. - 11
Solve for b: 3.5b - 4 = 10.
You can check by multiplying 3.5 by your answer and then subtracting 4.
Add 4 to both sides to get 3.5b = 14. Divide both sides by 3.5, so b = 4. - 12
A movie ticket costs $8, and a snack costs $3. Mia spent $35 on tickets and one snack. If x is the number of tickets she bought, write and solve an equation for x.
The equation is 8x + 3 = 35. Subtract 3 from both sides to get 8x = 32, then divide by 8, so x = 4. Mia bought 4 tickets. - 13
A taxi charges a $5 starting fee plus $2 per mile. The total cost is $23. If m is the number of miles, write and solve an equation for m.
The starting fee is added one time, and the mileage cost is repeated for each mile.
The equation is 2m + 5 = 23. Subtract 5 from both sides to get 2m = 18, then divide by 2, so m = 9. The taxi ride was 9 miles. - 14
Solve for q: (q - 4)/3 = 8.
Because the entire expression q - 4 is divided by 3, undo the division first.
Multiply both sides by 3 to get q - 4 = 24. Add 4 to both sides, so q = 28. - 15
A rectangle has a perimeter of 34 centimeters. Its length is 10 centimeters, and its width is w centimeters. Use the equation 2w + 20 = 34 to find the width.
Subtract 20 from both sides to get 2w = 14. Divide both sides by 2, so w = 7. The width is 7 centimeters.