Solving linear equations where brackets are used | Maths

Starter quiz

$3\over2$ is the ______ of $2\over3$ .
- opposite
- fraction
- reciprocal ✓
- product
Expand $7(2x-3)$ .
- $7x-21$
- $14x-3$
- $14x-21$ ✓
- $14x+21$
- $-14x-21$
Expand ${1\over5}(10x-25)$ .
- $50x-125$
- $50x+125$
- $2x-25$
- $2x+25$
- $2x-5$ ✓
The solution to $8y+20=4$ is $y=$ ______.
- '-2' ✓
Solve $7x-3=2x+12$ .
- $x=3$ ✓
- $x=2$
- $x=-2$
- $x=-3$
Solve $7x-3=2x+11$ .
- $5\over14$
- $5\over8$
- $8\over5$
- $14\over5$ ✓

$8(x+5)=5(2x-4)$ is an example of ______.
- an expression
- an unknown
- an equation ✓
- a substitution
Which of these show a correct method and solution for the equation $9(y-3)=45$ ?
- $y-3=45$ , therefore $y=48$
- $y-3=5$ , therefore $y=8$ ✓
- $9y-3=45$ , therefore $9y=48$ and $y={48\over9}$
- $9y-27=45$ , therefore $9y=72$ and $y=8$ ✓
- $9y-27=45$ , therefore $9y=18$ and $y=2$
The solution to $8(x+5)=5(2x-4)$ is $x=$ ______.
- '30' ✓
Solve $7(x+5)=5(2x-4)$ .
- $x=-{55\over3}$
- $x=-5$
- $x=5$
- $x={55\over3}$ ✓
Which is the most efficient start to solving the equation ${5\over4}(3x+1)=20$ ?
- multiply out the brackets
- divide both sides by $5$
- multiply both sides by $5\over4$
- multiply both sides by $4\over5$ ✓
- multiply both sides by $4$
The solution to the equation ${5\over4}(3x+1)=20$ is $x=$ ______.
- '5' ✓

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It is possible to divide by the coefficient of the bracket first when solving an equation.
When there are common factors this may be the most efficient method.
When the coefficient is a fraction it may be helpful to rewrite the equation.
It is possible to expand the bracket before solving an equation.
You will need to be able to make decisions about the most efficient method to a solution.

That all brackets have to be expanded before we solve an equation with brackets it in.

How would you solve $2y=50$ ? You would divide both sides by $2$ . So why not start with 'divide $2$ ' when solving $2(y-7)=50$ ?

Equation - An equation is used to show two expressions that are equal to each other.