Solving two step linear equations | Maths | Quizalize & Oak National Academy

Starter quiz

An equation is used to show two expressions that are ______ to each other.
- 'equal' ✓
Work out the value of $13+7+(−7)$
- $6$
- $7$
- $13$ ✓
- $20$
Work out the value of ${20 \over 4}$
- $4$
- $5$ ✓
- $16$
- $20$
- $80$
Solve the equation $x + 9 = 21$
- $x=9$
- $x=12$ ✓
- $x=21$
- $x=30$
Solve the equation $5x = 15$
- $x=3$ ✓
- $x=5$
- $x=10$
- $x=75$
Solve the equation $7x = 3$
- $x=−4$
- $x={3\over7}$ ✓
- $x={7\over3}$
- $x=21$
- It can't be solved because $7$ is not divisible by $3$

The solution to an equation is the value which, when substituted, maintains the ______ between the two expressions.
- 'equality' ✓
Which is the most useful additive first step to apply to both sides when solving $7y − 3=18$ ?
- $−3$
- $+3$ ✓
- $−7$
- $−18$
Solve $3y + 7 = 19$
- $y=3$
- $3y=12$
- $y=4$ ✓
- $y=12$
Which is the most useful multiplicative first step to apply to both sides when solving $6y−12=18$ ?
- $\div 2$
- $\div 3$
- $\div 6$ ✓
- $\times 3$
- $\times 6$
Match each equation to its solution.
- $2x+3=4$
  
  ⇔
  
  $x={1\over2}$ ✓
- $3x+2=4$
  
  ⇔
  
  $x={2\over3}$ ✓
- $2x+4=3$
  
  ⇔
  
  $x=−{1\over2}$ ✓
- $3x+4=2$
  
  ⇔
  
  $x=−{2\over3}$ ✓
- $4x+3=2$
  
  ⇔
  
  $x=−{1\over4}$ ✓
- $4x+2=3$
  
  ⇔
  
  $x={1\over4}$ ✓
$x=$ ______ is the solution to the equation ${x\over8}+{1\over4}={1\over2}$
- '2' ✓

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When an equation is in the form Ax + B = C you can solve by first subtracting B from both sides.
When an equation is in the form Ax + B = C you can solve by first dividing both sides by A.
These two options give the same solution.
In any particular situation one way may be more efficient than the other and it useful to think carefully about this.

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.