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

Let's solve in

ℝ

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

ⓘ Like terms are grouped by adding their coefficients:

\frac{3 x}{2} + x

\frac{5 x}{2}

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

Let's sum the fractions:

\frac{5 x}{2}

- 2

- \frac{1}{4}

- 2 x = 0

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

- 2 - \frac{1}{4}

\frac{4 \cdot (-2) - 1}{4}

■Like terms are grouped by adding their coefficients:

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

\frac{x}{2}

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

ⓘ Multiplications are done before additions and subtractions. A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

4 \cdot (-2)

-8

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

\frac{x}{2} + \frac{- 8 - 1}{4}

\frac{x \cdot 2 + (- 8 - 1)}{4}

\frac{x \cdot 2 + (- 8 - 1)}{4} = 0

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

- 8 - 1

-9

\frac{x \cdot 2 - 9}{4} = 0

⇥Let's solve in

ℝ

x \cdot 2 - 9 = 0

⇥

x \cdot 2 = 9

⇥ⓘ Both sides are divided by

2

▶Solution found:

x = \frac{9}{2}

The numeric value of:

x = \frac{9}{2}

equals:

▷

x = 4.5