½x + 1 = ¼x + 4
Let's solve a linear equation that has fractions in it. There's a clever first move that makes the rest easy.
Here's our equation: one-half x plus one equals one-fourth x plus four.
Look at the denominators — two and four. Their least common multiple is four. That's our magic number.
Multiply every term on both sides by four. That cancels the denominators and clears the fractions.
Now we have whole numbers: two x plus four equals x plus sixteen.
Subtract x from both sides to gather the x terms on the left.
That leaves x plus four equals sixteen.
Now subtract four from both sides to isolate x.
And we get x equals twelve.
Let's check by substituting. One-half of twelve plus one is seven. One-fourth of twelve plus four is also seven. Both sides match.
x equals twelve. Nice work clearing those fractions!