Key points
To solve A mathematical statement showing that two expressions are equal. The expressions are linked with the symbol =, a good understanding of A series or system of written symbols used to represent numbers, amounts or elements in mathematics. and In algebra substitute means to replace a letter (or variable) with a number. into A mathematical sentence expressed either numerically or symbolically made up of one or more terms. can be helpful.
An equation is a mathematical statement showing that two expressions are equal. The two expressions are linked with an equals symbol (=).
To solve an equation, the value of the unknown An unknown value, usually represented by a letter like π or π must be found. In the equation 3\(x\) + 4 = 25, the unknown variable is \(x\)
The unknown variable (often the letter \(x\)) can take any value, including decimal and negative values.
Solving equations with π on one side
An equation is like a set of scales that are in balance. The An element within an algebraic sentence. Elements (terms) are separated by + or - signs. on both sides are in balance because they represent the same amount or value.
To solve an equation, the value of the unknown variable needs to be found. It can be found by performing the same operation on each side of the equation until the value for \(x\) is known.
The opposite of a mathematical process. Eg, the inverse of Γ 5 is Γ· 5. The inverse operation undoes the original process. are used when deciding on the operation to use. The inverse operation for addition is subtraction and the inverse operation for multiplication is division.
Check your answer by substituting the solution back into the original equation.
Examples
Image caption, Solve the equation 3π + 4 = 25
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Question
Solve the equation.
- To work out the value of \(x\), add 3 to both sides of the equation.
2\(x\) β 3 + 3 = 2\(x\) and β7 + 3 = β4
This produces the equation 2\(x\) = β4
- To find the value of \(x\), divide both sides by 2
\( \frac{2x}{2}\) \(= x\) and \( \frac{-4}{2}\) = -2
Dividing both sides by 2 gives \(x\) = β2
- Check the answer by substituting \(x\) = β2 in the original equation.
2\(x\) β 3 = β7, 2 Γ β 2 β 3 = β4 β 3 = β7
This proves that the solution \(x\) = β2 is correct.
Select the correct first step to solve these equations
Practise solving equations with π on one side by selecting the correct first step.
Solving equations with two or more steps
To solve any equation, you need to find the value of the unknown variable by performing the same operations on both sides.
To solve an equation, more than one step may be needed to find the unknown variable.
Remember to check your answer by substituting the solution back into the original equation.
Examples
Image caption, Solve the equation.
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Question
There is a number, (\(n\)).
6 is added and then the result is multiplied by 2
The answer is 14
Write down the correct equation for this example.
Remember that in an equation, the unknown variable can take any value. In this example, the unknown variable is \(n\)
First, 6 is added to \(n\) to give \(n\) + 6
The result \(n\) + 6 is multiplied by 2
Brackets are essential to show that \(n\) + 6 is all multiplied by 2
The correct equation for this example is 2(\(n\) + 6) = 14
Practise solving equations with π on one side
Quiz
Practise solving equations with \(x\) on one side with this quiz. You may need a pen and paper to help you with your answers.
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More on Equations
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