New
New
Year 8
Many equations, one solution
I can understand that a family of linear equations can all have the same solution.
New
New
Year 8
Many equations, one solution
I can understand that a family of linear equations can all have the same solution.
Lesson details
Key learning points
- Starting from a single value for a variable you can write equations that are equivalent.
- A solution to a linear equation is a value that makes the two sides equal .
- All the equivalent equations will have the same solution.
Common misconception
Pupils may think a value has to be added to each term in an expression.
When adding a term to an expression we can write it as a single addition and then collect like terms if necessary. Show with numbers first
Keywords
Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Equation - An equation is used to show two expressions that are equal to each other.
Give pupils a simple equation e.g. x = 9 and see how many equivalent equations they can generate in a set time. For challenge you could ask them to generate ones with 2 steps, 3 steps, a division, a fraction etc.
Teacher tip
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
Loading...
Starter quiz
Download starter quiz
6 Questions
Q1.
This bar model represents the initial equation $$2x + 3 = 9$$. What needs to be done to the top bar to maintain equality?
Correct answer: $$+9$$
$$+9$$
$$+2x$$
Correct answer: $$+(2x+3)$$
$$+(2x+3)$$
$$\times 1$$
Correct answer: $$\times 2$$
$$\times 2$$
Q2.
Which of these calculations show '6 plus 3 all multiplied by 2'?
6 + 3 × 2
Correct answer: 2(6 + 3)
2(6 + 3)
2 × 6 + 3
Correct answer: 2 × 6 + 2 × 3
2 × 6 + 2 × 3
6 + 3 + 6
Q3.
Lucas manipulates the equation $$2x + 8 = 6$$. Which of these equations could he obtain and maintain equality?
Correct answer: $$x + 4 = 3$$
$$x + 4 = 3$$
Correct answer: $$2x + 10 = 8$$
$$2x + 10 = 8$$
$$10x + 8 = 30$$
$$2x = 6$$
Correct answer: $$4x + 8 = 2x + 6$$
$$4x + 8 = 2x + 6$$
Q4.
Which expression could fill the blank on the right hand side of this equation to maintain equality?
Correct answer: $$2x + 1$$
$$2x + 1$$
$$2x + 2$$
$$x + 4$$
Correct answer: $${2x + 4}\over 2$$
$${2x + 4}\over 2$$
Correct answer: $$x + 2$$
$$x + 2$$
Q5.
Which of these equations has a solution of $$x = 6$$?
$$x + 5 = −1$$
Correct answer: $$2x − 3 = 9$$
$$2x − 3 = 9$$
Correct answer: $$5 + 3x = 2x + 11$$
$$5 + 3x = 2x + 11$$
$$10 − x = 16$$
$$15 − 2x = 2x$$
Q6.
Which of these is a solution to the equation $$18 − 6x = 12 − 4x$$?
$$x = −4$$
$$x = −1$$
$$x = 0$$
$$x = 2$$
Correct answer: $$x = 3$$
$$x = 3$$
Exit quiz
Download exit quiz
6 Questions
Q1.
Which of these equations are equivalent to $$x = 5$$?
Correct answer: $$2x = 10$$
$$2x = 10$$
$$x − 2 = 7$$
Correct answer: $$x + 3 = 8$$
$$x + 3 = 8$$
Correct answer: $$2x = x + 5$$
$$2x = x + 5$$
$$x + 5 = 0$$
Q2.
If $$8x + 4 = 12$$, which of these equations has maintained equality?
$$2x + 4 = 3$$
$$2x + 1 = 12$$
Correct answer: $${1\over 4}(8x + 4) = {12\over 4}$$
$${1\over 4}(8x + 4) = {12\over 4}$$
$$8x + 1 = 3$$
Correct answer: $${{8x + 4}\over 4} = 3 $$
$${{8x + 4}\over 4} = 3 $$
Q3.
Which of these equations are equivalent to $$12x + 2 = 8x − 6$$?
Correct answer: $$12x + 8 = 8x$$
$$12x + 8 = 8x$$
$$12x = 8x − 4$$
Correct answer: $$6x + 1 = 4x − 3$$
$$6x + 1 = 4x − 3$$
Correct answer: $$10x + 2 = 6x − 6$$
$$10x + 2 = 6x − 6$$
$$3x + 1 = 2x + 3$$
Q4.
Which of these is a solution to the equation $$5x − 5 = 9 − 2x$$?
$$x = −2$$
$$x = −1$$
$$x = 0$$
$$x = 1$$
Correct answer: $$x = 2$$
$$x = 2$$
Q5.
What operation is missing from this diagram?
$$\times 4$$
Correct answer: $$\times {1\over 4}$$
$$\times {1\over 4}$$
Correct answer: $$\div 4$$
$$\div 4$$
$$ + (−9)$$
Q6.
What operation is missing from this diagram?
$$\times 2$$
$$+ (−3)$$
$$+ x$$
$$+ (x + 3)$$
Correct answer: $$+ (x − 3)$$
$$+ (x − 3)$$