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.