(3x-6)/2 =(4x-2)/4 — step-by-step solution

Let's solve in

ℝ

\frac{3 x - 6}{2} = \frac{4 x - 2}{4}

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

\frac{4 x - 2}{4}

\frac{2 x - 1}{2}

\frac{3 x - 6}{2} = \frac{2 x - 1}{2}

ⓘ A fraction whose numerator is a sum splits term by term, (a + b)/c = a/c + b/c:

\frac{2 x - 1}{2}

x - \frac{1}{2}

\frac{3 x - 6}{2} = x - \frac{1}{2}

Let's add fractions:

\frac{3 x - 6}{2} - x + \frac{1}{2} = 0

ⅰ

\frac{3 x - 6}{2} - x

\frac{(3 x - 6) + 2 \cdot (- x)}{2}

\frac{(3 x - 6) + 2 \cdot (- x)}{2} + \frac{1}{2} = 0

ⓘ The minus sign is placed in front of the product:

2 \cdot (- x)

- 2 x

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

\frac{3 x - 6 - 2 x}{2} + \frac{1}{2}

\frac{(3 x - 6 - 2 x) + 1}{2}

\frac{(3 x - 6 - 2 x) + 1}{2} = 0

ⓘ The numerator and the denominator are computed before the division:

- 6 + 1

-5

■Like terms are grouped by adding their coefficients:

3 x - 2 x

x

\frac{x - 5}{2} = 0

⇥Let's solve in

ℝ

x - 5 = 0

▶Solution found:

x = 5