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Algebra Basics Worksheet

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Algebra Basics Worksheet

Use letters to stand for numbers. Show your working when you solve an equation.

Algebraic Expressions

An expression can include numbers, operation signs and variables. Like terms have the same variable.

1.Which options are algebraic expressions? Select all that apply.

4m + 9
16 − 5
3p − 8
21

2.Evaluate 5n − 3 when n = 4.

3.Simplify 6x + 2x.

4.Simplify 9y − 4y + 6.

5.Simplify 3a + 2b + 4a − 5b.

Solving Equations

Keep an equation balanced by doing the same operation to both sides.

6.Find x if x + 9 = 17.

7.Solve 4y = 28.

8.Solve 3a − 4 = 14.

9.Substitute your answer for a into the original equation 3a − 4 = 14 to check it. Show the substitution and state whether both sides are equal.

Algebra in Situations

10.For a school play, Cooper buys several prop badges costing $4 each. He spends $28 altogether. Write an equation using b for the number of badges, then solve it.

11.A rectangular stage platform has a perimeter of 30 m and a width of 5 m. Using P = 2l + 2w, calculate its length.

12.Solve 3(x − 2) = x + 8. Expand the brackets first.

13.Arjun is planning a school-play ticket bundle. Each bundle costs $6, plus a one-off $12 booking fee. The total is $42. Write an equation for the number of bundles, n, and work out how many bundles are bought.