Solving complex linear equations involving brackets | Maths

Starter quiz

The command word to turn $-2(5-3y)$ into $6y-10$ is ______.
- 'expand' ✓
- 'solve'
- 'simplify'
- 'substitute'
The command words to turn $5(x+7)-3(x+2)$ into $2x+29$ are ______.
- 'expand and solve'
- 'expand and simplify' ✓
- 'substitute and simplify'
- 'substitute and solve'
Simplify $4x+9+x-11$
- $4x^2-2$
- $4x-2$
- $5x+2$
- $5x-2$ ✓
- $5x-20$
Expand and simplify $8(x-3)+3(5x+7)$ .
- $8x-3+15x+7=23x+4$
- $8x+24+15x+21=23x+45$
- $8x-24-15x+21=-7x-3$
- $8x-24+15x+21=23x-3$ ✓
- $8x-24+15x+21=23x+3$
Which of these expressions can be simplified before the brackets are expanded?
- $3(x-7)+2(x-7)$ ✓
- $3(x-7)+7(x-3)$
- $3(2x+5)+2(2x+5)$ ✓
- $3(2d+5)+2(2e+5)$
- $3(5-x)+2(5-x)$ ✓
Which of the below are expressions for the perimeter of this rectangle?
- $(7x+3)+(4x+1)$
- $2(7x+3)+2(4x+1)$ ✓
- $2(7x + 3 + 4x+1)$ ✓
- $7x+3=4x+1$

You can expand brackets in the expression $2(y+9)+2(3y-7)$ to get the expression $2y+18+6y-14$ . You now have like terms that can be ______.
- evaluated
- substracted
- simplified ✓
- solved
The perimeter of this rectangle is $154$ units. Which equation can be used to find $x$ ?
- $9x+14=154$
- $2(4x+15) + 2(5x-1)=154$ ✓
- $4x+15=5x-1=154$
- $2(4x+15) + 2(5x-1)$
The perimeter of this rectangle is $154$ units. The value of $x$ is ______.
- '7' ✓
Which of these are accurate first steps when solving $4(3x-1)-2(x+2)=72$ ?
- $12x-1-2x+2=72$
- $12x-4-2x+4=72$
- $12x-4-2x-4=72$ ✓
- $2(3x-1)-(x+2)=72$
- $2(3x-1)-(x+2)=36$ ✓
The solution to $4(3x-1)-2(x+2)=72$ is $x=$ ______.
- '8' ✓
The solution to $8(3x-6)-5(3x-6)=9$ is $x=$ ______.
- '3' ✓

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Brackets where an expression is multiplied by a term can be expanded.
Like terms can then be collected so the equation is in a form that can be solved.
Multiple identical expressions can be collected together to simplify an equation.

That there is only one way to solve any given equation.

In maths we will often see multiple ways to solve the same one problem. To be able to use multiple methods is a demonstration of fluency.

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