x/3 =(5x-9)/4-(x-1)/2 — step-by-step solution

1) Let's solve in

ℝ

\frac{x}{3} = \frac{5 x - 9}{4} - \frac{x - 1}{2}

\frac{x}{3} = \frac{5 x - 9}{4} + \frac{- x + 1}{2}

\frac{x}{3} = \frac{(5 x - 9) + 2 \cdot (- x + 1)}{4}

\frac{x}{3} = \frac{5 x - 9 + 2 \cdot (- x + 1)}{4}

2) Let's add fractions:

\frac{x}{3} - \frac{5 x - 9 + 2 \cdot (- x + 1)}{4} = 0

\frac{x \cdot 4 - (5 x - 9 + 2 \cdot (- x + 1)) \cdot 3}{3 \cdot 4} = 0

\frac{x \cdot 4 - (5 x - 9 + 2 \cdot (- x + 1)) \cdot 3}{12} = 0

3) Let's solve in

ℝ

x \cdot 4 - (5 x - 9 + 2 \cdot (- x + 1)) \cdot 3 = 0

ℹ

2 \cdot (- x + 1)

2 \cdot (- x) + 2

‖

- (5 x - 9 + (2 \cdot (- x) + 2)) \cdot 3

- (15 x - 27 + (2 \cdot (- x) + 2) \cdot 3)

x \cdot 4 - (15 x - 27 + (2 \cdot (- x) + 2) \cdot 3) = 0

x \cdot 4

- 15 x

+ 27

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

ℹ

x \cdot 4 - 15 x

-11 x

‖

- (- 2 x + 2)

2 x - 2

- 11 x + 27 + (2 x - 2) \cdot 3 = 0

- 11 x + 27 + (6 x - 6) = 0

ℹ

27 - 6

21

‖

- 11 x + 6 x

-5 x

- 5 x + 21 = 0

- 5 x = -21

5 x = 21

▶Solution obtained:

x = \frac{21}{5}

4) The numeric value of:

x = \frac{21}{5}

is:

▷

x = 4.2