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Year 8 in England

7th grade algebra

17 7th grade algebra skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheetRiddle puzzle on screenBingo

Two-step equations

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: 7x − 14 = −49

  1. 7x − 14 = −49
  2. 7x = −35
  3. x = −5

Answer: x = -5

Builds on: One-step equations, Add and subtract integers

Leads to: Ratio problems with algebra, Solve linear inequalities, Write and solve equations from words, Equations with the unknown on both sides

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Expand brackets (distributive property)

CCSS 6.EE.A.3CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Expand: 4(x + 9)

  1. 4 × x = 4x
  2. 4 × 9 = 36
  3. 4x + 36

Answer: 4x+36

Builds on: Simplify expressions: like terms, Multiply and divide integers

Leads to: Factorise linear expressions, Equations with the unknown on both sides, Multiply binomials (expand double brackets), Expand brackets with a negative multiplier

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Factorise linear expressions

CCSS 6.EE.A.3CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

What is the highest common factor of the terms in 8x + 12?

  1. 8x + 12 = 4(2x + 3)

Answer: 4

Builds on: Expand brackets (distributive property), Greatest common factor and least common multiple

Leads to: Factorise quadratics x² + bx + c, Factorise fully, including variable and negative common factors, Take out the greatest common factor of a polynomial

Print a worksheet✏️ Write on screenFlashcards

Solve linear inequalities

CCSS 7.EE.B.4.BEngland: GCSE Foundation AlgebraEngland: GCSE Higher Algebra

Example

Solve: 7x + 10 < 80

  1. 7x < 70
  2. x < 10

Answer: x < 10

Builds on: Two-step equations, Inequalities: meaning and solutions

Leads to: Compound inequalities and integer solutions, Quadratic inequalities, Solve multi-step inequalities, including reversing the sign, Find domains of functions with roots and fractions

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Write and solve equations from words

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Mei thinks of a number, multiplies it by 7 and adds 17. The answer is 94. Find the number.

  1. 7x + 17 = 94
  2. 7x = 77
  3. x = 11

Answer: x = 11

Builds on: Two-step equations, Write algebraic expressions

Leads to: Systems of equations: word problems

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Collect like terms with negative coefficients

CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Simplify −3x − 6 − 7x + 8.

  1. (−3 + (−7))x + (−6 + 8)
  2. −10x + 2

Answer: -10x+2

Builds on: Simplify expressions: like terms, Add integers using sign rules

Leads to: Expand two brackets and simplify

Print a worksheet✏️ Write on screenFlashcards

Expand brackets with a negative multiplier

CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Expand −5(x − 8).

  1. −5 × x = −5x
  2. −5 × (−8) = 40
  3. −5x + 40

Answer: -5x+40

Builds on: Expand brackets (distributive property), Multiply integers, including three factors and powers

Leads to: Expand two brackets and simplify, Solve equations with brackets and x on both sides

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Expand two brackets and simplify

CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Expand and simplify 5(x + 9) + 2(x + 4).

  1. 5x + 45 + 2x + 8
  2. 7x + 53

Answer: 7x+53

Builds on: Expand brackets with a negative multiplier, Collect like terms with negative coefficients

Print a worksheet✏️ Write on screenFlashcards

Factorise fully, including variable and negative common factors

CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Factorise −2x − 18 by taking out a negative common factor.

  1. −2 × x = −2x, −2 × 9 = −18
  2. −2(x + 9)

Answer: −2(x + 9)

Builds on: Factorise linear expressions

Print a worksheet✏️ Write on screenFlashcards

Solve two-step equations with negative numbers

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: x − 11 = −17

  1. x = −17 + 11 = −6
  2. x = −6 ÷ 1 = −6

Answer: x = -6

Builds on: Two-step equations, Divide integers and find missing factors

Leads to: Solve equations of the form p(x + q) = r, Solve two-step equations with a division, Write and solve two-step equations from real situations, Find and fix mistakes in equation solutions

Print a worksheet✏️ Write on screenFlashcards

Solve equations of the form p(x + q) = r

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: 2(x + 9) = 36

  1. x + 9 = 36 ÷ 2 = 18
  2. x = 9

Answer: x = 9

Builds on: Solve two-step equations with negative numbers, Expand brackets (distributive property)

Print a worksheet✏️ Write on screenFlashcards

Solve two-step equations with a division

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: x/3 − 2 = −3

  1. x/3 = −1
  2. x = −1 × 3 = −3

Answer: x = -3

Builds on: Solve two-step equations with negative numbers

Print a worksheet✏️ Write on screenFlashcards

Write and solve two-step equations from real situations

CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

A phone plan costs $19 per month plus $8 per GB of data. One month's bill was $51. How many GB were used?

  1. 8g = 51 − 19 = 32
  2. g = 32 ÷ 8 = 4

Answer: 4

Builds on: Solve two-step equations with negative numbers

Print a worksheet✏️ Write on screenFlashcards

Solve one-step inequalities, including dividing by a negative

CCSS 7.EE.B.4.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: x + 6 ≤ 2

  1. x ≤ −4

Answer: x ≤ −4

Builds on: Inequalities: meaning and solutions, Divide integers and find missing factors

Leads to: Solve two-step inequalities

Print a worksheet✏️ Write on screenFlashcards

Solve two-step inequalities

CCSS 7.EE.B.4.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve: 3x − 6 < 3

  1. 3x < 9
  2. x < 3

Answer: x < 3

Builds on: Solve one-step inequalities, including dividing by a negative

Leads to: Solve inequality problems about budgets and limits

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Solve inequality problems about budgets and limits

CCSS 7.EE.B.4.BEngland: KS3 Algebra

Example

Mei has $59 at a fair. Entry costs $6 and each ride costs $4. What is the greatest number of rides Mei can go on?

  1. 4r ≤ 53
  2. r ≤ 13.25
  3. At most 13 rides

Answer: 13

Builds on: Solve two-step inequalities

Print a worksheet✏️ Write on screenFlashcards

Find and fix mistakes in equation solutions

CCSS 7.EE.B.4.AEngland: KS3 Algebra

Example

Solving 3x + 6 = 3: Step 1: 3x = -3. Step 2: x = −1. Where is the first mistake?

  1. 3x = 3 − 6 = -3
  2. x = -3 ÷ 3 = −1
  3. No mistake

Answer: No mistake

Builds on: Solve two-step equations with negative numbers

Print a worksheet✏️ Write on screenFlashcards

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7th grade Algebra: Practice and Worksheets | Eurekami