Solve 280=1/2left(a+1/3a+4right)*14

$$280 = \frac{ 1 }{ 2 } \left( a+ \frac{ 1 }{ 3 } a+4 \right) \times 14$$

Solve for a

$$a=27$$

Steps for Solving Linear Equation

Combine a and \frac{1}{3}a to get \frac{4}{3}a.

$$280=\frac{1}{2}\left(\frac{4}{3}a+4\right)\times 14$$

Multiply \frac{1}{2} and 14 to get \frac{14}{2}.

$$280=\frac{14}{2}\left(\frac{4}{3}a+4\right)$$

Divide 14 by 2 to get 7.

$$280=7\left(\frac{4}{3}a+4\right)$$

Use the distributive property to multiply 7 by \frac{4}{3}a+4.

$$280=7\times \frac{4}{3}a+28$$

Express 7\times \frac{4}{3} as a single fraction.

$$280=\frac{7\times 4}{3}a+28$$

Multiply 7 and 4 to get 28.

$$280=\frac{28}{3}a+28$$

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

$$\frac{28}{3}a+28=280$$

Subtract 28 from both sides.

$$\frac{28}{3}a=280-28$$

Subtract 28 from 280 to get 252.

$$\frac{28}{3}a=252$$

Multiply both sides by \frac{3}{28}, the reciprocal of \frac{28}{3}.

$$a=252\times \frac{3}{28}$$

Express 252\times \frac{3}{28} as a single fraction.

$$a=\frac{252\times 3}{28}$$

Multiply 252 and 3 to get 756.

$$a=\frac{756}{28}$$

Divide 756 by 28 to get 27.

$$a=27$$