Linear equations with variables on both sides · lesson

Variables on both sides

💡 Move all the x terms to one side and all the numbers to the other, then divide.

If x is on both sides, subtract one x term from both sides. Now x is on just one side.

Then move the numbers to the other side. Divide by the coefficient last.

It's often easiest to move the smaller x term.

🧠 Let's work it out

Solve 7x − 4 = 3x + 32.

What do you think comes next?

💡 Distribute and combine like terms on each side before you move terms across.

If there are parentheses, multiply them out first. Then combine like terms on each side.

Now it looks like a both-sides equation. Solve it the same way.

🧠 Let's work it out

Solve 2(x + 4) = 5x − 16.

What do you think comes next?

💡 Multiply every term by 10 to clear the decimals, or solve with the decimals as they are.

Decimals work like any other number. But it's easier to clear them first.

Multiply every term on both sides by 10 (or 100). The equation stays balanced.

🧠 Let's work it out

Solve 0.3x + 4 = 0.1x + 7.

What do you think comes next?

💡 Call the unknown number n, write each side of the story, and set them equal.

Story puzzles say what happens to a number. Let n be the number.

Write what is done to it as one side. Write what it equals as the other side. Then solve.

🧠 Let's work it out

A number is doubled, and then 5 is added. That equals the number plus 14. What is the number?

What do you think comes next?