Practice Maths

Topic Review — Linear Equations and Inequalities

Mixed Practice — L12 – L14

This review covers solving linear equations, equations with fractions, and linear inequalities. Try each question before checking your answers.

Review Questions

  1. Solving linear equations. Fluency

    1. Solve: 3x + 7 = 22
    2. Solve: 5(y − 2) = 15
    3. Solve: 4m − 3 = 2m + 9
    4. Solve: −3(2k + 1) = 9
    5. Solve: 7 − 2x = −5

  2. Equations with fractions. Fluency

    1. Solve: (x + 3)/4 = 5
    2. Solve: x/2 + x/5 = 7
    3. Solve: (3y − 1)/2 = (y + 5)/3
    4. Solve: 4/x = 8
    5. Solve: x/3 − x/4 = 2

  3. Linear inequalities. Fluency

    1. Solve and graph: 2x − 5 > 3
    2. Solve and graph: −3y + 6 ≤ 0
    3. Solve: 4m + 1 ≥ 2m − 7
    4. Solve: 5 − (x + 1) < 2x − 2
    5. Solve the compound inequality: −3 ≤ 2x + 1 < 9

  4. Mixed equations and forming algebraic expressions. Understanding

    1. The sum of three consecutive even integers is 54. Let the smallest be n. Form and solve an equation to find all three integers.
    2. Solve (2x + 1)/3 + (x − 2)/4 = 3. Show each step clearly.
    3. A student solves −2x + 4 > 10 and writes x > −3. Find and explain their error, then give the correct solution.
    4. Is x = 4 a solution to 3x − 2 ≥ 5x − 10? Show working and explain.

  5. Problem solving — equations and inequalities in context. Problem Solving

    1. Two friends, Yuki and Ben, each start saving money. Yuki has $40 and saves $15 per week. Ben has $100 and saves $8 per week. After how many weeks will they have the same amount? Write and solve an equation.
    2. A rectangular paddock has a perimeter of 86 m. Its length is 7 m more than twice its width. Find the dimensions of the paddock by writing and solving an equation.
    3. A phone plan charges a flat fee of $12 per month plus $0.08 per text message. Anika’s budget is at most $30 per month. Write and solve an inequality to find the maximum number of texts she can send.
    4. Mei needs a score of at least 75% to pass her maths subject. She has completed 3 assessments with scores of 70%, 80%, and 68%. Her final assessment is worth the same as each previous one. What is the minimum score Mei needs on her final assessment to pass? Write and solve an inequality.
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