Linear Equations in One Variable
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Linear Equations and Their Solutions
Part of: Equations and solutions
An equation says that two expressions are equal. The expression on the left of the equals sign is the LHS and the one on the right is the RHS. A value of the variable that makes both sides equal is a solution. In this chapter the variable has power 1, so the equations are linear.
Why it matters. Seeing an equation as a balance makes every later step meaningful. Children who only memorise 'move and change sign' often slip in longer problems.
Try it in two minutes
- Draw a balance with 3 + 4 on one side and 7 on the other. Ask: is it balanced?
- Hide one number with your hand, for example x + 4 = 9, and ask what x must be.
- Add 2 to both sides and ask if the balance still holds.
Try at home. Ask your child to make up an equation whose solution is 6, and check it by putting 6 in.
Variable on Both Sides
Part of: Equations and solutions
When x appears on both sides, such as 3x + 1 = x + 9, we first collect the x terms on one side by subtracting x from both sides. This is the same as moving the term across the equals sign and changing its sign. Then we solve the simpler equation as usual.
Why it matters. Many real situations compare two quantities that both change, such as two phone plans or two ages. Solving with the variable on both sides is the first step to handling these problems.
Try it in two minutes
- Write 2x + 3 = x + 7 on paper. Ask your child what to do to remove the x on the right side.
- Solve it together and then check by putting x back in both sides.
- Ask your child to make up a similar equation with the solution 5.
Try at home. Ask your child to solve 4x - 2 = x + 10 and to check the answer.
Clearing Fractions
Part of: Simplifying equations
Fractions in an equation can be removed by multiplying both sides by the LCM of the denominators. For x/2 + x/3 = 10 the LCM is 6, so we get 3x + 2x = 60. Remember to multiply every term, including the plain numbers.
Why it matters. Equations with fractions look harder, but once cleared they are ordinary equations. Children who skip multiplying a term often get wrong answers, so this habit matters.
Try it in two minutes
- Write x/2 + 3 = 7 on paper and ask: what number clears the fraction?
- Multiply every term by 2 and see the equation x + 6 = 14.
- Try x/2 + x/3 = 10 with 6 and check the answer by putting it back.
Try at home. Ask your child to find the LCM of 4 and 6 and use it to solve x/4 + x/6 = 5.
Brackets, Simplifying and Checking
Part of: Simplifying equations
Some equations have brackets or like terms to tidy first. We open brackets using distributivity, combine like terms on each side, then solve as before. At the end we check the answer by putting it in the original equation.
Why it matters. Real problems and exam questions rarely arrive in the neat form. Tidying first, and checking at the end, saves marks and builds confidence that the answer is right.
Try it in two minutes
- Write 2(x + 3) = x + 10 and ask your child to open the bracket.
- Solve for x together and check by putting the value into both sides.
- Ask: if the two sides do not match, what should we do?
Try at home. Ask your child to make an equation with a bracket whose solution is 4, and to check it.
What your child will practise
- Brackets, Simplifying and Checking: Ocean Puzzle (Clue Puzzle)
- Clearing Fractions: Ocean Quick Fire (Quick Fire)
- Linear Equations and Their Solutions: Jungle Quick Fire (Quick Fire)
- Linear Equations and Their Solutions: Mission Control Sort (Sort It Out)
- Variable on Both Sides: Lab Explorer Quest (Match It Up)
- Quiz: Brackets, Simplifying and Checking (8 questions)
- Quiz: Clearing Fractions (8 questions)
- Quiz: Linear Equations and Their Solutions (8 questions)
- Quiz: Variable on Both Sides (8 questions)