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.

## Lesson details

### Key learning points

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

### 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.

### 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

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).

## Video

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## Starter quiz

Download starter quiz

### 6 Questions

Q1.

$$1\over5$$ is the __________ of 5.

additive inverse

multiplier

opposite

product

Correct answer: reciprocal

reciprocal

Q2.

Expand $$4(5x - 2)$$.

$$4x - 8$$

$$9x - 8$$

$$9x - 2$$

Correct answer: $$20x - 8$$

$$20x - 8$$

$$20x - 2$$

Q3.

The solution to $$y + 8 = 5$$ is when $$y=$$ .

Correct Answer: -3, negative 3, negative three, - 3

-3, negative 3, negative three, - 3

Q4.

The solution to $$3y = 15$$ is when $$y=$$ .

Correct Answer: 5, five

5, five

Q5.

Which of these equations are equivalent to the equation $$5x + 20 = 25$$ ?

$$5x = -5$$

Correct answer: $$5x = 5$$

$$5x = 5$$

$$5x = 25$$

Correct answer: $$ x + 4 = 5$$

$$ x + 4 = 5$$

$$x + 20 = 5$$

Q6.

Which of these equations are equivalent to the equation $$4x + 14 = 2x - 7$$ ?

Correct answer: $$2x + 14 = -7$$

$$2x + 14 = -7$$

$$6x + 14 = -7$$

$$2x + 7 = x - 7$$

Correct answer: $$14 = -2x - 7$$

$$14 = -2x - 7$$

$$4x = 2x + 7$$

## Exit quiz

Download exit quiz

### 6 Questions

Q1.

The solution to the equation $$3(x + 4) = 33$$ is when $$x =$$ .

Correct Answer: 7, seven

7, seven

Q2.

Which of these equations are equivalent to $$2(4x - 3) = 18$$ ?

$$2x - 3 = 9$$

$$4x - 3 = 18$$

Correct answer: $$4x - 3 = 9$$

$$4x - 3 = 9$$

Correct answer: $$8x - 6 = 18$$

$$8x - 6 = 18$$

$$8x - 6 = 9$$

Q3.

The solution to the equation $$5(x - 3) = 2(3x - 8)$$ is when $$x=$$ .

Correct Answer: 1, one

1, one

Q4.

Select the equations that are equivalent to $$5(2x - 3) = 10$$.

Correct answer: $$3(2x - 3) + 2(2x - 3) = 10$$

$$3(2x - 3) + 2(2x - 3) = 10$$

$$3(2x - 3) = 2(2x - 3) + 10$$

Correct answer: $$7(2x - 3) - 2(2x - 3) = 10$$

$$7(2x - 3) - 2(2x - 3) = 10$$

Correct answer: $$ 8(2x - 3) = 3(2x - 3) + 10$$

$$ 8(2x - 3) = 3(2x - 3) + 10$$

$$10(4x + 1) - 5(2x + 4) = 10$$

Q5.

The solution to $$3(2x + 5) + 5(x - 6) = 29$$ is when $$x =$$ .

Correct Answer: 4, four

4, four

Q6.

The solution to $$7(2x - 3) - 5(2x - 3) = 42$$ is when $$x = $$ .

Correct Answer: 12, twelve

12, twelve