Solve 15+t/frac{145-t{2}}=3/2

$$\frac { 15 + t } { \frac { 145 - t } { 2 } } = \frac { 3 } { 2 }$$

Solve for t

$$t = \frac{375}{7} = 53\frac{4}{7} \approx 53.571428571$$

Steps for Solving Linear Equation

Divide 15+t by \frac{145-t}{2} by multiplying 15+t by the reciprocal of \frac{145-t}{2}.

$$\frac{\left(15+t\right)\times 2}{145-t}=\frac{3}{2}$$

Use the distributive property to multiply 15+t by 2.

$$\frac{30+2t}{145-t}=\frac{3}{2}$$

Variable t cannot be equal to 145 since division by zero is not defined. Multiply both sides of the equation by 2\left(t-145\right), the least common multiple of 145-t,2.

$$-2\left(30+2t\right)=3\left(t-145\right)$$

Use the distributive property to multiply -2 by 30+2t.

$$-60-4t=3\left(t-145\right)$$

Use the distributive property to multiply 3 by t-145.

$$-60-4t=3t-435$$

Subtract 3t from both sides.

$$-60-4t-3t=-435$$

Combine -4t and -3t to get -7t.

$$-60-7t=-435$$

Add 60 to both sides.

$$-7t=-435+60$$

Add -435 and 60 to get -375.

$$-7t=-375$$

Divide both sides by -7.

$$t=\frac{-375}{-7}$$

Fraction \frac{-375}{-7} can be simplified to \frac{375}{7} by removing the negative sign from both the numerator and the denominator.

$$t=\frac{375}{7}$$