Solve 18+8t/frac{5{8}}=8-t/10

$$\frac { 18 + 8 t } { \frac { 5 } { 8 } } = \frac { 8 - t } { 10 }$$

Solve for t

$$t = -\frac{280}{129} = -2\frac{22}{129} \approx -2.170542636$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10.

$$10\times \frac{18+8t}{\frac{5}{8}}=8-t$$

Divide each term of 18+8t by \frac{5}{8} to get \frac{18}{\frac{5}{8}}+\frac{8t}{\frac{5}{8}}.

$$10\left(\frac{18}{\frac{5}{8}}+\frac{8t}{\frac{5}{8}}\right)=8-t$$

Divide 18 by \frac{5}{8} by multiplying 18 by the reciprocal of \frac{5}{8}.

$$10\left(18\times \frac{8}{5}+\frac{8t}{\frac{5}{8}}\right)=8-t$$

Express 18\times \frac{8}{5} as a single fraction.

$$10\left(\frac{18\times 8}{5}+\frac{8t}{\frac{5}{8}}\right)=8-t$$

Multiply 18 and 8 to get 144.

$$10\left(\frac{144}{5}+\frac{8t}{\frac{5}{8}}\right)=8-t$$

Divide 8t by \frac{5}{8} to get \frac{64}{5}t.

$$10\left(\frac{144}{5}+\frac{64}{5}t\right)=8-t$$

Use the distributive property to multiply 10 by \frac{144}{5}+\frac{64}{5}t.

$$10\times \frac{144}{5}+10\times \frac{64}{5}t=8-t$$

Express 10\times \frac{144}{5} as a single fraction.

$$\frac{10\times 144}{5}+10\times \frac{64}{5}t=8-t$$

Multiply 10 and 144 to get 1440.

$$\frac{1440}{5}+10\times \frac{64}{5}t=8-t$$

Divide 1440 by 5 to get 288.

$$288+10\times \frac{64}{5}t=8-t$$

Express 10\times \frac{64}{5} as a single fraction.

$$288+\frac{10\times 64}{5}t=8-t$$

Multiply 10 and 64 to get 640.

$$288+\frac{640}{5}t=8-t$$

Divide 640 by 5 to get 128.

$$288+128t=8-t$$

Add t to both sides.

$$288+128t+t=8$$

Combine 128t and t to get 129t.

$$288+129t=8$$

Subtract 288 from both sides.

$$129t=8-288$$

Subtract 288 from 8 to get -280.

$$129t=-280$$

Divide both sides by 129.

$$t=\frac{-280}{129}$$

Fraction \frac{-280}{129} can be rewritten as -\frac{280}{129} by extracting the negative sign.

$$t=-\frac{280}{129}$$