Solve -3/v+5=-2/3v+15-1

$$- \frac { 3 } { v + 5 } = - \frac { 2 } { 3 v + 15 } - 1$$

Solve for v

$$v = -\frac{8}{3} = -2\frac{2}{3} \approx -2.666666667$$

Steps for Solving Linear Equation

Variable v cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by 3\left(v+5\right), the least common multiple of v+5,3v+15.

$$-3\times 3=-2+3\left(v+5\right)\left(-1\right)$$

Multiply -3 and 3 to get -9.

$$-9=-2+3\left(v+5\right)\left(-1\right)$$

Multiply 3 and -1 to get -3.

$$-9=-2-3\left(v+5\right)$$

Use the distributive property to multiply -3 by v+5.

$$-9=-2-3v-15$$

Subtract 15 from -2 to get -17.

$$-9=-17-3v$$

Swap sides so that all variable terms are on the left hand side.

$$-17-3v=-9$$

Add 17 to both sides.

$$-3v=-9+17$$

Add -9 and 17 to get 8.

$$-3v=8$$

Divide both sides by -3.

$$v=\frac{8}{-3}$$

Fraction \frac{8}{-3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$v=-\frac{8}{3}$$