Early Algebra: Practice Set 2
Early Algebra: Practice Set 2 gives further practice at forming and solving equations, extending into two-step equations where the letter appears on both sides, equations built from word problems, and equations that come from a shape's perimeter or a sequence's nth term. It follows directly on from the first Early Algebra topic.
Method
- Read the problem carefully and decide what the unknown number represents, then give it a letter.
- Turn each piece of information in the problem into an algebraic term or expression, using brackets to keep grouped quantities together.
- Combine the expressions into a single equation, making sure both sides represent the same total or relationship described in the problem.
- Solve the equation using inverse operations, undoing addition and subtraction before multiplication and division, or by collecting all letter terms on one side first if the letter appears twice.
- Substitute your solution back into the original equation, not just the simplified version, to check both sides are equal.
- Reread the question to check whether it wants the value of the letter itself or a related quantity built from it, such as a shape's perimeter.
Worked example
Sam thinks of a number. He doubles it, then adds 7. His answer is the same as the number multiplied by 5, minus 11. What number did Sam think of?
- Let x represent the number Sam thought of.
- Write an equation for both descriptions: doubling and adding 7 gives 2x + 7; multiplying by 5 and subtracting 11 gives 5x - 11. Since these are equal: 2x + 7 = 5x - 11.
- Subtract 2x from both sides: 7 = 3x - 11.
- Add 11 to both sides: 18 = 3x.
- Divide both sides by 3: x = 6.
- Check: 2(6) + 7 = 19 and 5(6) - 11 = 19, so both sides match. Sam's number is 6.
Practice questions
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Q1Solve 2x + 5 = 3x - 4.Show answer
Answer: x = 9 (5 + 4 = 3x - 2x)
Q2A number is doubled and then 3 is subtracted, giving the same result as adding 9 to the number. Find the number.Show answer
Answer: 12 (2x - 3 = x + 9)
Q3Simplify 5(x - 2) + 3(x + 4).Show answer
Answer: 8x + 2
Q4Solve 4(x + 1) = 2(x + 9).Show answer
Answer: x = 7 (4x + 4 = 2x + 18, so 2x = 14)
Q5A rectangle has length (2x + 1) cm and width (x + 3) cm. Its perimeter is 38 cm. Form and solve an equation to find x.Show answer
Answer: x = 5 (2[(2x+1)+(x+3)] = 38 gives 6x + 8 = 38)
Q6Three consecutive whole numbers add up to 72. Form an equation using n for the smallest number, and solve it to find the three numbers.Show answer
Answer: 23, 24 and 25 (n + (n+1) + (n+2) = 72 gives 3n + 3 = 72, so n = 23)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Priya thinks of a number, n. She multiplies it by 3, then adds 8. Ben thinks of the same number, doubles it, then adds 20. Their two results are equal. (a) Write an equation in terms of n. (b) Solve your equation to find n.
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A triangle has three angles: the smallest angle is x degrees, the second angle is (x + 20) degrees, and the third angle is twice the smallest angle. (a) Write an expression, in terms of x, for the sum of the three angles. (b) Use the fact that angles in a triangle sum to 180 degrees to form and solve an equation for x. (c) State the size of each of the three angles.
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A number machine takes an input, multiplies it by 4, then subtracts 9, to give an output of 31. (a) Write an equation using x for the input. (b) Solve the equation to find x. (c) A second input produces an output of 55 using the same machine. Find this second input.
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Free printable worksheet
Want more practice on paper? Download the early algebra: practice set 2 worksheet pack - 10 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 12 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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