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

1) Let's solve in

ℝ

\frac{4 x - 3}{3} = \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{4 x - 3}{3} = x - \frac{1}{2}

2) Let's add fractions:

\frac{4 x - 3}{3} - x + \frac{1}{2} = 0

ⅰ

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

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

\frac{(4 x - 3) + 3 \cdot (- x)}{3} + \frac{1}{2} = 0

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

3 \cdot (- x)

- 3 x

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

\frac{4 x - 3 - 3 x}{3} + \frac{1}{2}

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

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

ⓘ Like terms are grouped by adding their coefficients:

4 x - 3 x

x

ⅰ

3 \cdot 2

6

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

Let's solve in

ℝ

(x - 3) \cdot 2 + 3 = 0

ⓘ Expand by multiplying each term inside the parentheses:

(x - 3) \cdot 2

x \cdot 2 - 6

x \cdot 2 - 6 + 3 = 0

ⓘ Start from

-6

and move forward

3

on the number line, getting closer to zero:

- 6 + 3

-3

x \cdot 2 - 3 = 0

x \cdot 2 = 3

ⓘ Both sides are divided by

2

▶Solution found:

x = \frac{3}{2}

3) The numeric value of:

x = \frac{3}{2}

equals:

▷

x = 1.5