Solve 7/(2a) = 8/(-a-5)

Evaluate

\frac{7}{2 a} = \frac{8}{- a - 5}

Find the domain

More Steps

\frac{7}{2 a} = \frac{8}{- a - 5}, a \in (- \infty, - 5) \cup (- 5, 0) \cup (0, + \infty)

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{7}{2 a} = - \frac{8}{a + 5}

Rewrite the expression

\frac{7}{2 a} = \frac{- 8}{a + 5}

Cross multiply

7 (a + 5) = 2 a (- 8)

Simplify the equation

7 (a + 5) = - 16 a

Expand the expression

More Steps

7 a + 35 = - 16 a

Move the variable to the left side

7 a + 35 + 16 a = 0

Add the terms

More Steps

23 a + 35 = 0

Move the constant to the right side

23 a = 0 - 35

Removing 0 doesn't change the value,so remove it from the expression

23 a = - 35

Divide both sides

\frac{23 a}{23} = \frac{- 35}{23}

Divide the numbers

a = \frac{- 35}{23}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

a = - \frac{35}{23}

Check if the solution is in the defined range

a = - \frac{35}{23}, a \in (- \infty, - 5) \cup (- 5, 0) \cup (0, + \infty)

Solution

a = - \frac{35}{23}

Alternative Form

a \approx - 1.521739

Solve the equation