Key points
An equation is like a set of scales that are in balance.
- An A mathematical statement showing that two expressions are equal. The expressions are linked with the symbol = 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 either side of the equals sign (=) have the same value as each other.
- Equations need to stay in balance. Do the same thing to both sides to keep the equation balanced, for example adding or subtracting the same amount from each side.
- When a An unknown value, usually represented by a letter like π or π is A number that we do not know. They are commonly used in algebra, and sometimes referred to as variable and represented by symbols such as π or π it is often given a value of \(x\), although it is important to remember that any letter can be used to represent an unknown value.
- The unknown variable (often the letter \(x\)) can take any value, including decimal and negative values.
An equation is like a set of scales that are in balance.
Solving equations when both unknown terms are positive
- If both unknown variables are positive, the first step is to subtract one of these \(x\) terms.
- Subtracting the \(x\) term which has the smaller A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. Eg, 5 is the coefficient of 5π means that negative terms can be avoided.
- The \(x\) term with the smallest coefficient can appear on the left or the right of the = sign.
- This will reduce the number of terms and lead to a new A mathematical statement showing that two expressions are equal. The expressions are linked with the symbol = (still balanced) with just one A number that we do not know. They are commonly used in algebra, and sometimes referred to as variable and represented by symbols such as π or π variable.
- Check the solution by substituting the final answer back into the original equation.
Example
Image caption, The equation 3π + 4 = π + 12 can be represented by the diagram above. The equals sign between the two sets of terms shows that the equation is in balance.
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Question
Find the value of the unknown term \(x\) when 2\(x\) + 5 = \(x\) + 8
- Subtract an \(x\) term from each side to leave \(x\) + 5 = 8
- Subtract 5 from each side.
This gives the solution that \(x\) = 3
Solving equations when one unknown term is negative
- If one unknown An unknown value, usually represented by a letter like π or π is negative, the first step is to add one of the \(x\) .
- Adding an \(x\) term helps avoid unknown values with negative A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. Eg, 5 is the coefficient of 5π.
- The \(x\) term with a negative coefficient can appear on the left or the right of the equals sign.
- This will reduce the number of terms and lead to a new equation that is still in balance, with just one unknown variable.
Example
Image caption, The equation 9 - 2π = π + 3 can be represented by the diagram above. The equals sign between the two sets of terms shows that the equation is in balance.
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Question
Find the value of the unknown term \(x\) when \(x\) + 5 = 17 β 3\(x\)
- Add 3\(x\) to each side to leave 4\(x\) + 5 = 17
- Subtract 5 from each side, resulting in 4\(x\) = 12
- Divide both sides of the equation by 4
This gives the solution that \(x\) = 3
Practise solving equations with π on both sides
Quiz
Practise solving equations with \(x\) on both sides 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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