Rearranging to solve linear equations | Maths | Quizalize & Oak National Academy

Starter quiz

In order to maintain ______ in an equation, any manipulation must be applied to both sides of the equation.
- equality ✓
- positivity
- solutions
- variables
What must be added to both sides of the equation to turn $x=7$ into $x+3=10$ ?
- $3$ ✓
- $3x$
- $7$
- $10$
What must be added to both sides of the equation to turn $x+3=10$ into $5x+3=4x+10$ ?
- $4$
- $5$
- $x$
- $4x$ ✓
- $5x$
$(−4)$ is added to both sides of the equation $9x+4=6$ . What is the resulting equation?
- $x=−4$
- $9x=6$
- $9x=2$ ✓
- $5x=2$
$y=$ ______ is the solution to the equation $29=6y−7$
- '6' ✓
Solve $2y−4=−8$
- $y=6$
- $y=−6$
- $y=2$
- $y=−2$ ✓
- $y=−4$

An equation is used to show two ______ that are equal to each other.
- equalities
- solutions
- variables
- expressions ✓
What equation is represented by this balance model?
- $3x=1$
- $2x=3$
- $5x=4$
- $x+1=x+3$
- $3x+1=2x+3$ ✓
Which additive step will manipulate the equation $7x−3=2x+18$ so that it has unknowns on only one side?
- $+(−7x)$ ✓
- $+(3)$
- $+(−2x)$ ✓
- $+(−18)$
- $+(−x)$
Add $3x$ to both sides of the equation $x+2=7−3x$
- $x+5=10−3x$
- $3x+2=7$
- $4x+2=7−6x$
- $4x+2=7$ ✓
- $4x+5=10$
$x=$ ______ is the solution to the equation $5x+21=9x+5$
- '4' ✓
Solve $6x−1=7−3x$
- $x={8\over{9}}$ ✓
- $x={8\over{3}}$
- $x=−{8\over{9}}$
- $x={9\over{8}}$
- $x={6\over{9}}$

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Any linear equation written in the form Ax + B = C can be solved.
Like terms can be collected onto one side of an equation in order to write it in the form Ax + B = C.
An equation that had unknowns on both sides can then be solved.

To subtract from both the variable and numerical terms when subtracting from both sides.

To subtract $2$ from $5x+3$ leaves $5x+1$ , not $3x+1$ . Use visual representations like balance scales and bar models to show this.

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