After solving a linear equation, how can you check your answer to see if it is correct?

After solving a linear equation, you should substitute your answer back into the equation to check if it is correct. This is a quick way to spot if you have made any mistakes.

IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1FlashcardsAlgebraSolving Linear Equations

Solving Linear Equations (Edexcel IGCSE Maths A (Modular))

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FrontSolving Linear Equations
What is the greatest power of $x$ in a linear equation?
FrontSolving Linear Equations
What are inverse operations?
BackSolving Linear Equations
Inverse operations are the opposite operations to what has already happened to the variable.
E.g. In the expression $4 x$ , $x$ is being multiplied by 4.
The inverse operation is to divide by 4.
Examples of inverse operations are:
Add and subtract
Multiply and divide
Square and take the square root

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Cards in this collection (15)

What is the greatest power of $x$ in a linear equation?
The greatest power of $x$ in a linear equation is 1.
There is no term in x² or any higher power.
What does 'isolate the variable' mean?
Isolate the variable means to get the variable term, e.g. $x$ , by itself on one side of the equation.
What are inverse operations?
Inverse operations are the opposite operations to what has already happened to the variable.
E.g. In the expression $4 x$ , $x$ is being multiplied by 4.
The inverse operation is to divide by 4.
Examples of inverse operations are:
- Add and subtract
- Multiply and divide
- Square and take the square root
True or False?
To solve a linear equation, e.g. $3 x + 4 = 13$ , you need to isolate the variable by carrying out inverse operations to both sides.
True.
To solve a linear equation, you need to isolate the variable, (get the letter on its own), by carrying out inverse operations to both sides.
E.g.
$3 x + 4 = 13 \begin{matrix} - 4 & - 4 \end{matrix} 3 x = 9 \div 3 \div 3 x = 3$
What is the order of inverse operations to solve a linear equation of the form $a x + b = c$ to find $x$ .
To solve a linear equation of the form $a x + b = c$ :
- First subtract $b$ from both sides
- Then divide both sides by $a$
True or False?
If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.
E.g. $8 x + 7 = 2 x + 11$ .
True.
If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.
E.g.
$\begin{array}{rcl} 8 x + 7 & = & 2 x + 11 \\ 6 x + 7 & = & 11 \end{array}$
What is the first step to solve a linear equation with brackets?
E.g. $4 (x + 6) = 32$ .
The first step to solve a linear equation with brackets is to expand the brackets (on both sides if necessary).
E.g.
$\begin{array}{rcl} 4 (x + 6) & = & 32 \\ 4 x + 24 & = & 32 \end{array}$
What is the first step to solve a linear equation with fractions?
E.g. $\frac{x + 9}{2} = \frac{3 x - 1}{4}$ .
The first step to solve a linear equation with fractions is to remove the fractions by multiplying both sides by the denominators.
E.g.
$\begin{array}{rcl} \frac{x + 9}{2} & = & \frac{3 x - 1}{4} \\ 4 (x + 9) & = & 2 (3 x - 1) \end{array}$
After solving a linear equation, how can you check your answer to see if it is correct?
After solving a linear equation, you should substitute your answer back into the equation to check if it is correct.
This is a quick way to spot if you have made any mistakes.
Use algebra to represent double the amount of a quantity, given that $x$ is the initial quantity.
Double the amount of a quantity $x$ can be written as $2 x$ .
Use algebra to represent half the amount of a quantity, given that $x$ is the initial quantity.
Half the amount of a quantity $x$ can be written as $\frac{1}{2} x$ or $\frac{x}{2}$ or $0.5 x$ .
Use algebra to represent five more than a quantity, given that $x$ is the initial quantity.
Five more than a quantity $x$ can be written as $x + 5$ .
This is not the same as $5 x$ .
Use algebra to represent ten lots of a quantity, given that $x$ is the initial quantity.
Ten lots of a quantity $x$ can be written as $10 x$ .
This is not the same as $x + 10$ .
True or False?
If my sister is 2 years younger than me, then $x$ is my age and $x - 2$ is her age.
True.
If my sister is 2 years younger than me, then $x$ is my age and $x - 2$ is her age.
It is also true to say that $y + 2$ is my age and $y$ is her age.
Three bags contain $x$ , $x + 5$ and $x + 10$ marbles each.
If there are 75 marbles in total, explain how to form an equation.
Three bags contain $x$ , $x + 5$ and $x + 10$ marbles each.
If there are 75 marbles in total, then an equation can be formed by adding all the quantities up and setting them equal to 75.
This gives $x + (x + 5) + (x + 10) = 75$ .
Examiners want to see this full equation (before simplifying or solving).

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