m/6 =(m+1)/5 — step-by-step solution

Let's solve in

ℝ

\frac{m}{6} = \frac{m + 1}{5}

Let's sum the fractions:

\frac{m}{6} - \frac{m + 1}{5} = 0

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

\frac{m}{6} - \frac{m + 1}{5}

\frac{m \cdot 5 - (m + 1) \cdot 6}{6 \cdot 5}

\frac{m \cdot 5 - (m + 1) \cdot 6}{6 \cdot 5} = 0

ⅰ

6 \cdot 5

30

\frac{m \cdot 5 - (m + 1) \cdot 6}{30} = 0

⇥Let's solve in

ℝ

m \cdot 5 - (m + 1) \cdot 6 = 0

⇥ⓘ Expand by multiplying each term inside the parentheses:

- (m + 1) \cdot 6

- (m \cdot 6 + 6)

⇥

m \cdot 5 - (m \cdot 6 + 6) = 0

⇥ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (m \cdot 6 + 6)

- m \cdot 6 - 6

⇥

m \cdot 5 - m \cdot 6 - 6 = 0

⇥ⓘ Like terms are grouped by adding their coefficients:

m \cdot 5 - m \cdot 6

- m

⇥

- m - 6 = 0

⇥ⓘ We add

6

to both sides

⇥

- m = 6

⇥ⓘ The sign of both sides is changed

▶Solution found:

m = -6