Many equations, one solution | Maths | Quizalize & Oak National Academy

Starter quiz

This bar model represents the initial equation $2x + 3 = 9$ . What needs to be done to the top bar to maintain equality?
- $+9$ ✓
- $+2x$
- $+(2x+3)$ ✓
- $\times 1$
- $\times 2$ ✓
Which of these calculations show '6 plus 3 all multiplied by 2'?
- 6 + 3 × 2
- 2(6 + 3) ✓
- 2 × 6 + 3
- 2 × 6 + 2 × 3 ✓
- 6 + 3 + 6
Lucas manipulates the equation $2x + 8 = 6$ . Which of these equations could he obtain and maintain equality?
- $x + 4 = 3$ ✓
- $2x + 10 = 8$ ✓
- $10x + 8 = 30$
- $2x = 6$
- $4x + 8 = 2x + 6$ ✓
Which expression could fill the blank on the right hand side of this equation to maintain equality?
- $2x + 1$ ✓
- $2x + 2$
- $x + 4$
- ${2x + 4}\over 2$ ✓
- $x + 2$ ✓
Which of these equations has a solution of $x = 6$ ?
- $x + 5 = −1$
- $2x − 3 = 9$ ✓
- $5 + 3x = 2x + 11$ ✓
- $10 − x = 16$
- $15 − 2x = 2x$
Which of these is a solution to the equation $18 − 6x = 12 − 4x$ ?
- $x = −4$
- $x = −1$
- $x = 0$
- $x = 2$
- $x = 3$ ✓

Which of these equations are equivalent to $x = 5$ ?
- $2x = 10$ ✓
- $x − 2 = 7$
- $x + 3 = 8$ ✓
- $2x = x + 5$ ✓
- $x + 5 = 0$
If $8x + 4 = 12$ , which of these equations has maintained equality?
- $2x + 4 = 3$
- $2x + 1 = 12$
- ${1\over 4}(8x + 4) = {12\over 4}$ ✓
- $8x + 1 = 3$
- ${{8x + 4}\over 4} = 3$ ✓
Which of these equations are equivalent to $12x + 2 = 8x − 6$ ?
- $12x + 8 = 8x$ ✓
- $12x = 8x − 4$
- $6x + 1 = 4x − 3$ ✓
- $10x + 2 = 6x − 6$ ✓
- $3x + 1 = 2x + 3$
Which of these is a solution to the equation $5x − 5 = 9 − 2x$ ?
- $x = −2$
- $x = −1$
- $x = 0$
- $x = 1$
- $x = 2$ ✓
What operation is missing from this diagram?
- $\times 4$
- $\times {1\over 4}$ ✓
- $\div 4$ ✓
- $+ (−9)$
What operation is missing from this diagram?
- $\times 2$
- $+ (−3)$
- $+ x$
- $+ (x + 3)$
- $+ (x − 3)$ ✓

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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.

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

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.