Solve -20/7(33/4a+2/7)+12/7a=frac{4091}{49}

$$- \frac { 20 } { 7 } ( \frac { 33 } { 4 } a + \frac { 2 } { 7 } ) + \frac { 12 } { 7 } a = \frac { 4091 } { 49 }$$

Solve for a

$$a = -\frac{27}{7} = -3\frac{6}{7} \approx -3.857142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{20}{7} by \frac{33}{4}a+\frac{2}{7}.

$$-\frac{20}{7}\times \frac{33}{4}a-\frac{20}{7}\times \frac{2}{7}+\frac{12}{7}a=\frac{4091}{49}$$

Multiply -\frac{20}{7} times \frac{33}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-20\times 33}{7\times 4}a-\frac{20}{7}\times \frac{2}{7}+\frac{12}{7}a=\frac{4091}{49}$$

Do the multiplications in the fraction \frac{-20\times 33}{7\times 4}.

$$\frac{-660}{28}a-\frac{20}{7}\times \frac{2}{7}+\frac{12}{7}a=\frac{4091}{49}$$

Reduce the fraction \frac{-660}{28} to lowest terms by extracting and canceling out 4.

$$-\frac{165}{7}a-\frac{20}{7}\times \frac{2}{7}+\frac{12}{7}a=\frac{4091}{49}$$

Multiply -\frac{20}{7} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{165}{7}a+\frac{-20\times 2}{7\times 7}+\frac{12}{7}a=\frac{4091}{49}$$

Do the multiplications in the fraction \frac{-20\times 2}{7\times 7}.

$$-\frac{165}{7}a+\frac{-40}{49}+\frac{12}{7}a=\frac{4091}{49}$$

Fraction \frac{-40}{49} can be rewritten as -\frac{40}{49} by extracting the negative sign.

$$-\frac{165}{7}a-\frac{40}{49}+\frac{12}{7}a=\frac{4091}{49}$$

Combine -\frac{165}{7}a and \frac{12}{7}a to get -\frac{153}{7}a.

$$-\frac{153}{7}a-\frac{40}{49}=\frac{4091}{49}$$

Add \frac{40}{49} to both sides.

$$-\frac{153}{7}a=\frac{4091}{49}+\frac{40}{49}$$

Since \frac{4091}{49} and \frac{40}{49} have the same denominator, add them by adding their numerators.

$$-\frac{153}{7}a=\frac{4091+40}{49}$$

Add 4091 and 40 to get 4131.

$$-\frac{153}{7}a=\frac{4131}{49}$$

Multiply both sides by -\frac{7}{153}, the reciprocal of -\frac{153}{7}.

$$a=\frac{4131}{49}\left(-\frac{7}{153}\right)$$

Multiply \frac{4131}{49} times -\frac{7}{153} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{4131\left(-7\right)}{49\times 153}$$

Do the multiplications in the fraction \frac{4131\left(-7\right)}{49\times 153}.

$$a=\frac{-28917}{7497}$$

Reduce the fraction \frac{-28917}{7497} to lowest terms by extracting and canceling out 1071.

$$a=-\frac{27}{7}$$