Solve 20*4.185*302=left(90.67*4.185+20*4.185+62.3xright)305.5-left(90.67*4.185+62.3xright)306.5

$$20 \cdot 4.185 \cdot 302 = \left( 90.67 \cdot 4.185+20 \cdot 4.185+62.3x \right) 305.5- \left( 90.67 \cdot 4.185+62.3x \right) 306.5$$

Solve for x

$$x = -\frac{1730079}{1246000} = -1\frac{484079}{1246000} \approx -1.388506421$$

Steps for Solving Linear Equation

Multiply 20 and 4.185 to get 83.7.

$$83.7\times 302=\left(90.67\times 4.185+20\times 4.185+62.3x\right)\times 305.5-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Multiply 83.7 and 302 to get 25277.4.

$$25277.4=\left(90.67\times 4.185+20\times 4.185+62.3x\right)\times 305.5-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Multiply 90.67 and 4.185 to get 379.45395.

$$25277.4=\left(379.45395+20\times 4.185+62.3x\right)\times 305.5-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Multiply 20 and 4.185 to get 83.7.

$$25277.4=\left(379.45395+83.7+62.3x\right)\times 305.5-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Add 379.45395 and 83.7 to get 463.15395.

$$25277.4=\left(463.15395+62.3x\right)\times 305.5-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Use the distributive property to multiply 463.15395+62.3x by 305.5.

$$25277.4=141493.531725+19032.65x-\left(90.67\times 4.185+62.3x\right)\times 306.5$$

Multiply 90.67 and 4.185 to get 379.45395.

$$25277.4=141493.531725+19032.65x-\left(379.45395+62.3x\right)\times 306.5$$

Use the distributive property to multiply 379.45395+62.3x by 306.5.

$$25277.4=141493.531725+19032.65x-\left(116302.635675+19094.95x\right)$$

To find the opposite of 116302.635675+19094.95x, find the opposite of each term.

$$25277.4=141493.531725+19032.65x-116302.635675-19094.95x$$

Subtract 116302.635675 from 141493.531725 to get 25190.89605.

$$25277.4=25190.89605+19032.65x-19094.95x$$

Combine 19032.65x and -19094.95x to get -62.3x.

$$25277.4=25190.89605-62.3x$$

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

$$25190.89605-62.3x=25277.4$$

Subtract 25190.89605 from both sides.

$$-62.3x=25277.4-25190.89605$$

Subtract 25190.89605 from 25277.4 to get 86.50395.

$$-62.3x=86.50395$$

Divide both sides by -62.3.

$$x=\frac{86.50395}{-62.3}$$

Expand \frac{86.50395}{-62.3} by multiplying both numerator and the denominator by 100000.

$$x=\frac{8650395}{-6230000}$$

Reduce the fraction \frac{8650395}{-6230000} to lowest terms by extracting and canceling out 5.

$$x=-\frac{1730079}{1246000}$$