3z+1/2 =z+9/2 — step-by-step solution

Let's solve in

ℝ

3 z + \frac{1}{2} = z + \frac{9}{2}

ⓘ We subtract

\frac{1}{2}

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

\frac{9}{2} - \frac{1}{2}

\frac{9 - 1}{2}

3 z = z + \frac{9 - 1}{2}

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

9 - 1

8

3 z = z + \frac{8}{2}

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

2

, their greatest common divisor:

\frac{8}{2}

4

3 z = z + 4

ⓘ We subtract

z

from both sides

3 z - z = 4

ⓘ Like terms are grouped by adding their coefficients:

3 z - z

2 z

2 z = 4

ⓘ Both sides are divided by

2

z = \frac{4}{2}

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

2

, their greatest common divisor:

\frac{4}{2}

2

▶Solution obtained:

z = 2