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

Let's solve in

ℝ

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

Let's add fractions:

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

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

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

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

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

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 4

8

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

\frac{3 \cdot (x + 1) - 8 x}{4} + 3

\frac{(3 \cdot (x + 1) - 8 x) + 3 \cdot 4}{4}

\frac{(3 \cdot (x + 1) - 8 x) + 3 \cdot 4}{4} = 0

ⓘ Multiplications are done before additions and subtractions:

3 \cdot 4

12

\frac{3 \cdot (x + 1) - 8 x + 12}{4} = 0

⇥Let's solve in

ℝ

3 \cdot (x + 1) - 8 x + 12 = 0

⇥ⓘ Expand by multiplying each term inside the parentheses:

3 \cdot (x + 1)

3 x + 3

⇥

3 x

+ 3

- 8 x

+ 12 = 0

⇥ⓘ Start from

3

and move forward

12

on the number line:

3 + 12

15

■Like terms are grouped by adding their coefficients:

3 x - 8 x

-5 x

⇥

- 5 x + 15 = 0

⇥

5 x = 15

⇥ⓘ Both sides are divided by

5

⇥

x = \frac{15}{5}

⇥ⓘ We simplify the fraction by dividing the numerator and the denominator by

5

, their greatest common divisor:

\frac{15}{5}

3

▶Solution found:

x = 3