Expression or equation?
An expression, such as 3x + 4, describes a value. It does not say what x must be. An equation, such as 3x + 4 = 19, tells us that two expressions have the same value.
In 3x, the 3 is multiplying x. Think “three equal groups of the unknown number.” The equals sign tells you the total on the left balances the total on the right.
Worked example: solve 3x + 4 = 19
Start by undoing the added 4. Subtract 4 from both sides: 3x + 4 − 4 = 19 − 4. This leaves 3x = 15.
Now undo multiplication by 3. Divide both sides by 3: 3x ÷ 3 = 15 ÷ 3. The result is x = 5.
Check by replacing x in the original equation: 3 × 5 + 4 = 15 + 4 = 19. Both sides match, so x = 5 is a solution.
Common places to slow down
- Keep the equals sign: write a complete equation on each line so it is clear what is balanced.
- Track negative signs: distinguish subtracting a number from a number that is itself negative.
- Follow the structure: undo addition or subtraction around the multiplied variable before dividing in a problem like 3x + 4 = 19.
- Substitute to check: put the solution into the original equation, not just the last line of your working.
Prepare for algebra with connected practice
Confidence with multiplication, division, fractions, and signed numbers makes equation work easier. If a calculation keeps interrupting the algebra, practice that calculation separately and return to the equation afterward.
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