1/4 x+1/2 = 3/4 x — step-by-step solution

⚠ 1/4 x+1/2 = 3/4 x is read as (1/4)*x+1/2 = (3/4)*x: use (1/4)*x to multiply by the following factor, use 1/(4*x) to include it in the denominator; use (3/4)*x to multiply by the following factor, use 3/(4*x) to include it in the denominator

Let's solve in

ℝ

\frac{1}{4} \cdot x + \frac{1}{2} = \frac{3}{4} \cdot x

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{1}{4} \cdot x

\frac{1 \cdot x}{4}

\frac{x}{4}

\frac{3}{4} \cdot x

\frac{3 x}{4}

■To add fractions, put them over the same denominator, then add the numerators:

\frac{x}{4} + \frac{1}{2}

\frac{x + 2}{4}

\frac{x + 2}{4} = \frac{3 x}{4}

Let's sum the fractions:

\frac{x + 2}{4} - \frac{3 x}{4} = 0

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{x + 2}{4} - \frac{3 x}{4}

\frac{(x + 2) - 3 x}{4}

\frac{(x + 2) - 3 x}{4} = 0

ⓘ Like terms are grouped by adding their coefficients:

x - 3 x

-2 x

\frac{- 2 x + 2}{4} = 0

ⓘ A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{- 2 x + 2}{4}

\frac{- x + 1}{2}

\frac{- x + 1}{2} = 0

⇥Let's solve in

ℝ

- x + 1 = 0

▶Solution found:

x = 1