Solve 4/t+7/3=1/2-4/3t

$$\frac { 4 } { t } + \frac { 7 } { 3 } = \frac { 1 } { 2 } - \frac { 4 } { 3 t }$$

Solve for t

$$t = -\frac{32}{11} = -2\frac{10}{11} \approx -2.909090909$$

Steps for Solving Linear Equation

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6t, the least common multiple of t,3,2,3t.

$$6\times 4+6t\times \frac{7}{3}=6t\times \frac{1}{2}-2\times 4$$

Multiply 6 and 4 to get 24.

$$24+6t\times \frac{7}{3}=6t\times \frac{1}{2}-2\times 4$$

Multiply 6 and \frac{7}{3} to get 14.

$$24+14t=6t\times \frac{1}{2}-2\times 4$$

Multiply 6 and \frac{1}{2} to get 3.

$$24+14t=3t-2\times 4$$

Multiply -2 and 4 to get -8.

$$24+14t=3t-8$$

Subtract 3t from both sides.

$$24+14t-3t=-8$$

Combine 14t and -3t to get 11t.

$$24+11t=-8$$

Subtract 24 from both sides.

$$11t=-8-24$$

Subtract 24 from -8 to get -32.

$$11t=-32$$

Divide both sides by 11.

$$t=\frac{-32}{11}$$

Fraction \frac{-32}{11} can be rewritten as -\frac{32}{11} by extracting the negative sign.

$$t=-\frac{32}{11}$$