Equations with fractions

Solve (x + 4)/2 = (x + 9)/4

The aim is to get x on its own. Whatever we do to one side, we do to the other, so the equation stays balanced. This one takes 4 steps.

(x + 4)/2 = (x + 9)/4The question.
Step 1: Multiply by 4 on both sides ×4

There are fractions. Multiply both sides by 4 to clear them: 4 is the smallest number that all the bottoms go into.
2(x + 4) = x + 9
Multiplying every term by the same number keeps the balance.
Step 2: Expand the brackets on both sides expand

Expand the brackets first, so you can see all the x terms.
2x + 8 = x + 9
Multiply the number outside by everything inside.
Step 3: Subtract x on both sides −x

There’s x on both sides. Take away x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.
x + 8 = 9
On the right, the x cancels out. Now there’s no x on the right.

You can add or take away x terms, just like numbers.
Step 4: Subtract 8 on both sides −8

On the left, the x part has + 8 with it. Take 8 away from both sides to get rid of it.
x = 1
On the left, the 8 cancels out. x is on its own. x = 1.

+ 8 is undone by − 8.

Answer: x = 1

Put x = 1 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 4)/2 → 5/2

Right side: (x + 9)/4 → 5/2

✓ Both sides are 5/2, so x = 1 is right.

Solve this one in Algebra Balance. You choose each step, and it explains what happened, with hints if you get stuck.