Checking and securing solving linear equations | Maths

Starter quiz

$1\over5$ is the __________ of 5.
- additive inverse
- multiplier
- opposite
- product
- reciprocal ✓
Expand $4(5x - 2)$ .
- $4x - 8$
- $9x - 8$
- $9x - 2$
- $20x - 8$ ✓
- $20x - 2$
The solution to $y + 8 = 5$ is when $y=$ ______.
- '-3' ✓
The solution to $3y = 15$ is when $y=$ ______.
- '5' ✓
Which of these equations are equivalent to the equation $5x + 20 = 25$ ?
- $5x = -5$
- $5x = 5$ ✓
- $5x = 25$
- $x + 4 = 5$ ✓
- $x + 20 = 5$
Which of these equations are equivalent to the equation $4x + 14 = 2x - 7$ ?
- $2x + 14 = -7$ ✓
- $6x + 14 = -7$
- $2x + 7 = x - 7$
- $14 = -2x - 7$ ✓
- $4x = 2x + 7$

The solution to the equation $3(x + 4) = 33$ is when $x =$ ______.
- '7' ✓
Which of these equations are equivalent to $2(4x - 3) = 18$ ?
- $2x - 3 = 9$
- $4x - 3 = 18$
- $4x - 3 = 9$ ✓
- $8x - 6 = 18$ ✓
- $8x - 6 = 9$
The solution to the equation $5(x - 3) = 2(3x - 8)$ is when $x=$ ______.
- '1' ✓
Select the equations that are equivalent to $5(2x - 3) = 10$ .
- $3(2x - 3) + 2(2x - 3) = 10$ ✓
- $3(2x - 3) = 2(2x - 3) + 10$
- $7(2x - 3) - 2(2x - 3) = 10$ ✓
- $8(2x - 3) = 3(2x - 3) + 10$ ✓
- $10(4x + 1) - 5(2x + 4) = 10$
The solution to $3(2x + 5) + 5(x - 6) = 29$ is when $x =$ ______.
- '4' ✓
The solution to $7(2x - 3) - 5(2x - 3) = 42$ is when $x =$ ______.
- '12' ✓

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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.

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.

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