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Mathematics · Grades 6–9

Expressions, equations and structure

Simplifying an expression and solving an equation are different tasks.

Make a worksheet

Understand the idea

Name the task

Simplifying an expression and solving an equation are different tasks.

Preserve equality

Apply equivalent operations to both sides when solving.

Use substitution

Check a proposed solution in the original equation.

Worked examples

Which is an equation rather than an expression?

An equation includes an equality statement.

3x + 2 = 11

Find x if 4(x − 2) = 20.

Divide by 4 to obtain x − 2 = 5, then add 2.

7

Try it yourself

  1. Which expression equals 5a + 2a − a?

    1. 8a
    2. 6a
    3. 7a
    4. 6a²

  2. Evaluate 2p² − 3 when p = −4.

  3. Expand −3(y − 5).

    1. 3y − 15
    2. −3y + 15
    3. −3y + 5
    4. −3y − 15

  4. A learner changes 2x + 5 = 13 to 2x = 18. Identify and correct the error.

Answers and marking notes

Answers and marking notes
  1. 6a

    Combine coefficients: 5 + 2 − 1 = 6.

  2. 29

    2 × 16 − 3 = 29.

  3. −3y + 15

    Multiply both terms by −3.

  4. They added 5 instead of subtracting it. Subtract 5 from both sides to obtain 2x = 8 and x = 4.

    Credit a correct equality-preserving explanation.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Preview material · independent educational review required. Grade bands are approximate, not official curriculum alignment.