Grade 8 Algebra: Solve Equations and Check Your Answers

By Future Kids Academy

When letters appear in maths, a child may feel they have lost the numbers they understood. In Grade 8 algebra, a letter can stand for an unknown value. Solving an equation means finding the value that makes both sides equal. A balanced equation gives us a practical way to reason through each step.

What does 4x mean?

4x means four multiplied by x. It does not mean forty-something, and it does not mean four plus x. In 4x + 17 = 85, the left side describes four equal amounts with seventeen added. The right side tells us the total is eighty-five.

Think of both sides as equal quantities on a balance. A valid solving step keeps that equality true. If you subtract seventeen from one side, subtract seventeen from the other side too.

A worked lesson example: 4x + 17 = 85

This equation is a worked example from the maths lessons. Instead of memorising “move it across and change the sign”, explain which operation you apply to both sides.

1. Read the operations. The unknown is multiplied by four, then seventeen is added.
2. Undo the addition. Subtract seventeen from both sides: 4x + 17 − 17 = 85 − 17.
3. Simplify. Seventeen minus seventeen is zero, leaving 4x = 68.
4. Undo the multiplication. Divide both sides by four: 4x ÷ 4 = 68 ÷ 4, so x = 17.
5. Check in the original equation. Replace x with seventeen: 4 × 17 + 17 = 68 + 17 = 85. The two sides match.

Why undo the operations in reverse order?

The expression builds a result by multiplying first and adding second. To recover the starting value, undo the final addition first, then undo the multiplication. This is like reversing a short set of instructions. It also makes the calculation simpler than dividing every term at the beginning.

A second example: 3x − 5 = 16

Add five to both sides to undo subtracting five: 3x − 5 + 5 = 16 + 5. This leaves 3x = 21. Divide both sides by three to get x = 7. Check: 3 × 7 − 5 = 21 − 5 = 16.

A common mistake: changing only one side

If your child subtracts seventeen from the left side but leaves eighty-five unchanged on the right, the balance has changed. Ask them to write the same operation underneath both sides before simplifying. Keep one line for each step so missing operations are visible.

Use a story to make the equation concrete

Four identical notebooks and a pen costing seventeen rand cost eighty-five rand altogether. If x represents the price of one notebook in rand, the equation is 4x + 17 = 85. Removing the pen’s cost leaves sixty-eight rand for four notebooks, so each notebook costs seventeen rand.

Ask your child to explain why the answer fits the story as well as the equation. Substitution is a useful habit: it checks the result directly rather than relying on confidence in the method.

More practice with answers

Write your working first, then open each answer to check your method.

Must x always mean the same number?

Within one equation, the same letter represents the same value. In a separate problem, x may have a different value.