New
New
Year 10
Foundation

Checking and securing understanding of solving and interpreting linear equations

I can solve complex linear equations involving brackets.

New
New
Year 10
Foundation

Checking and securing understanding of solving and interpreting linear equations

I can solve complex linear equations involving brackets.

Lesson details

Key learning points

  1. With linear equation involving brackets, there are two methods for addressing the brackets.
  2. You can expand the bracket (multiply out).
  3. You can divide each term.
  4. If there is a common factor across all terms, then division may be best.

Common misconception

If a linear equation involves brackets, these always have to be expanded first.

Get pupils to use knowledge of factors and collecting like terms to simplify problems.

Keywords

  • Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

  • Like terms - Like terms are terms that have the same set of variables and corresponding exponents.

Encourage clear working when forming and solving equations. When in context, pupils should be justifying their final answers and substituting to check they are correct.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Fully factorise the expression $$7y^2 - 14y$$
Correct answer: $$7y(y - 2)$$
$$7(y^2 - 2y)$$
$$y(7y - 14y)$$
Q2.
Fully factorise the expression $$2x^2 +7x + 3$$
$$(x + 3)(2x - 1)$$
$$(x + 3)(x + 1)$$
Correct answer: $$(x + 3)(2x + 1)$$
Q3.
A rectangle has side lengths of $$3x + 5$$ and $$2x - 3$$. Write an expression for the perimeter of the shape.
Correct Answer: 10x + 4
Q4.
A regular hexagon has side length $$3n - 4$$. Write an expression for the perimeter of the shape.
Correct Answer: 6(3n-4), 18n - 24
Q5.
A rectangle has side lengths of $$9x - y$$ and $$2y$$. Write an expression for the perimeter of the shape.
Correct Answer: 18x+2y, 2(9x+y)
Q6.
A square has side length $$15x - y$$. Write an expression for the perimeter of the shape.
Correct Answer: 4(15x - y), 60x - 4y

6 Questions

Q1.
What is the value of $$x$$ for $$5(x + 7) = 30$$
Correct Answer: -1
Q2.
What is the value of $$x$$ for $$\frac{3x - 7}{4} = 11$$
Correct Answer: 17
Q3.
What is the value of $$x$$ for $$2(x - 5) + 10 = 0$$
Correct Answer: 0
Q4.
What is the value of $$x$$ for $$\frac{x + 9}{5} - \frac{x - 3}{3} = 2$$
Correct Answer: 6
Q5.
What is the value of $$x$$ for $$4(3x - 2) + 2 = 3(2x + 4)$$
Correct Answer: 3
Q6.
What is the value of $$x$$ for $$\frac{5x + 15}{3} = \frac{2x - 2}{2}$$
Correct Answer: -9