Linear Equations & Polynomials

Solve equations and simplify simple polynomial expressions.

22 questions, free, marked as you go with a worked explanation on every one.

What this covers

The questions

  1. Solve for x: 3(x + 2) = 15
  2. Simplify: 4x + 3x = ?
  3. Solve for x: 2x - 5 = 3x + 1
  4. Expand: 2(x - 3) = ?
  5. Solve for x: x/3 + 2 = 7
  6. Solve for x: 5x - 8 = 12
  7. Simplify: 6x - 2x + 3x
  8. Expand 4(x + 1) - 2x and give the coefficient of x.
  9. Solve for x: 2x + 9 = 3
  10. Plot the point where the line y = 2x - 1 crosses x = 3.
  11. Plot the y-intercept of the line y = -x + 4.
  12. The perimeter of a rectangle is 54 cm. Its length is 3 cm more than twice its width. What is the width of the rectangle, in centimetres?
  13. Graph the line y = 2x - 1.
  14. What is the slope of the line shown?
  15. A rectangular garden has a width of (x + 2) metres and a length of 2x metres. If x = 5, what is the garden's perimeter, in metres?
  16. A square's perimeter is given by 8x cm. If x = 6, what is the square's side length, in centimetres?
  17. A rectangle has an area of 60 cm² and a width of 5 cm. What is its length, in centimetres?
  18. A rectangular field has a length that is triple its width. If the width is 12 m, what is the field's perimeter, in metres?
  19. Find the slope of the line through (2, 3) and (6, 11).
  20. What is the slope of the line y = 3x - 7?
  21. A line passes through these points: when x is 1, y is 4; when x is 2, y is 7; when x is 3, y is 10. What is the slope of this line?
  22. A tank is being filled with water. After 2 minutes it holds 14 L, and after 5 minutes it holds 32 L. What is the rate of filling, in litres per minute?

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