New
New
Year 9

Checking and securing solving linear equations

I can solve equations involving brackets.

New
New
Year 9

Checking and securing solving linear equations

I can solve equations involving brackets.

warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

Lesson details

Key learning points

  1. Equations containing a bracket multiplied by a term can be solve in two ways.
  2. If the term is a constant, it may be best to divide first.
  3. If the term is not a constant, it may be best to multiply first.
  4. If the term is a factor of every other term then division is likely to be simplest.

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

Common misconception

If equations contain brackets you always need to expand them before solving.

Try to encourage pupils to use their factors and multiples knowledge to decide if it is more efficient to expand first or not.

Encourage pupils to set out their working out in a clear way so that they can effectively compare efficiency of methods. Remind pupils they can substitute their solution back into the original equation to check if it is 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).

Lesson video

Loading...

6 Questions

Q1.
$$1\over5$$ is the __________ of 5.
additive inverse
multiplier
opposite
product
Correct answer: reciprocal
Q2.
Expand $$4(5x - 2)$$.
$$4x - 8$$
$$9x - 8$$
$$9x - 2$$
Correct answer: $$20x - 8$$
$$20x - 2$$
Q3.
The solution to $$y + 8 = 5$$ is when $$y=$$ .
Correct Answer: -3, negative 3, negative three, - 3
Q4.
The solution to $$3y = 15$$ is when $$y=$$ .
Correct Answer: 5, five
Q5.
Which of these equations are equivalent to the equation $$5x + 20 = 25$$ ?
$$5x = -5$$
Correct answer: $$5x = 5$$
$$5x = 25$$
Correct answer: $$ x + 4 = 5$$
$$x + 20 = 5$$
Q6.
Which of these equations are equivalent to the equation $$4x + 14 = 2x - 7$$ ?
Correct answer: $$2x + 14 = -7$$
$$6x + 14 = -7$$
$$2x + 7 = x - 7$$
Correct answer: $$14 = -2x - 7$$
$$4x = 2x + 7$$

6 Questions

Q1.
The solution to the equation $$3(x + 4) = 33$$ is when $$x =$$ .
Correct Answer: 7, seven
Q2.
Which of these equations are equivalent to $$2(4x - 3) = 18$$ ?
$$2x - 3 = 9$$
$$4x - 3 = 18$$
Correct answer: $$4x - 3 = 9$$
Correct answer: $$8x - 6 = 18$$
$$8x - 6 = 9$$
Q3.
The solution to the equation $$5(x - 3) = 2(3x - 8)$$ is when $$x=$$ .
Correct Answer: 1, one
Q4.
Select the equations that are equivalent to $$5(2x - 3) = 10$$.
Correct answer: $$3(2x - 3) + 2(2x - 3) = 10$$
$$3(2x - 3) = 2(2x - 3) + 10$$
Correct answer: $$7(2x - 3) - 2(2x - 3) = 10$$
Correct answer: $$ 8(2x - 3) = 3(2x - 3) + 10$$
$$10(4x + 1) - 5(2x + 4) = 10$$
Q5.
The solution to $$3(2x + 5) + 5(x - 6) = 29$$ is when $$x =$$ .
Correct Answer: 4, four
Q6.
The solution to $$7(2x - 3) - 5(2x - 3) = 42$$ is when $$x = $$ .
Correct Answer: 12, twelve