Linear equations Worked Solutions — GCSE Maths

Write down the equation

Start from the equation as given, and keep it balanced at every stage: whatever is done to one side must be done to the other.

Subtract $7$ from both sides

To get the $x$ term on its own, undo the $+7$ by doing the opposite to both sides.

Simplify

The $x$ term is now on its own on the left; the numbers have all been gathered on the right. The solution is $x = 5$.

Write down the equation

Start from the equation as given, and keep it balanced at every stage: whatever is done to one side must be done to the other.

Add $6$ to both sides

To get the $x$ term on its own, undo the $-6$ by doing the opposite to both sides.

Simplify

The $x$ term is now on its own on the left; the numbers have all been gathered on the right. The solution is $x = 17$.

Write down the equation

Start from the equation as given, and keep it balanced at every stage: whatever is done to one side must be done to the other.

Divide both sides by $5$

The $x$ is multiplied by $5$, so the inverse operation is to divide both sides by $5$.

Simplify

$40 \div 5 = 8$, so this is the value of $x$. The solution is $x = 8$.

Write down the equation

Start from the equation as given, and keep it balanced at every stage: whatever is done to one side must be done to the other.

Multiply every term by 4

The denominators are 4, and their lowest common multiple is 4. Multiply *every* term on *both* sides by 4 — miss one and the equation is no longer balanced.

Cancel the denominators

Each denominator divides exactly into 4, so the fractions disappear and only whole-number coefficients are left. The solution is $x = 28$.

Write down the equation

Start from the equation as given, and keep it balanced at every stage: whatever is done to one side must be done to the other.

Subtract $4$ from both sides

The $x$ term is now on its own on the left; the numbers have all been gathered on the right.

Divide both sides by $3$

$15 \div 3 = 5$, so this is the value of $x$. The solution is $x = 5$.