Solve 46=40+frac{229/2-(12+30+f_{1})}{65}*10

$$46 = 40 + \frac { 229 / 2 - ( 12 + 30 + f _ { 1 } ) } { 65 } \times 10$$

Solve for f_1

$$f_{1} = \frac{67}{2} = 33\frac{1}{2} = 33.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 65.

$$2990=2600+\left(\frac{229}{2}-\left(12+30+f_{1}\right)\right)\times 10$$

Add 12 and 30 to get 42.

$$2990=2600+\left(\frac{229}{2}-\left(42+f_{1}\right)\right)\times 10$$

To find the opposite of 42+f_{1}, find the opposite of each term.

$$2990=2600+\left(\frac{229}{2}-42-f_{1}\right)\times 10$$

Convert 42 to fraction \frac{84}{2}.

$$2990=2600+\left(\frac{229}{2}-\frac{84}{2}-f_{1}\right)\times 10$$

Since \frac{229}{2} and \frac{84}{2} have the same denominator, subtract them by subtracting their numerators.

$$2990=2600+\left(\frac{229-84}{2}-f_{1}\right)\times 10$$

Subtract 84 from 229 to get 145.

$$2990=2600+\left(\frac{145}{2}-f_{1}\right)\times 10$$

Use the distributive property to multiply \frac{145}{2}-f_{1} by 10.

$$2990=2600+\frac{145}{2}\times 10-10f_{1}$$

Express \frac{145}{2}\times 10 as a single fraction.

$$2990=2600+\frac{145\times 10}{2}-10f_{1}$$

Multiply 145 and 10 to get 1450.

$$2990=2600+\frac{1450}{2}-10f_{1}$$

Divide 1450 by 2 to get 725.

$$2990=2600+725-10f_{1}$$

Add 2600 and 725 to get 3325.

$$2990=3325-10f_{1}$$

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

$$3325-10f_{1}=2990$$

Subtract 3325 from both sides.

$$-10f_{1}=2990-3325$$

Subtract 3325 from 2990 to get -335.

$$-10f_{1}=-335$$

Divide both sides by -10.

$$f_{1}=\frac{-335}{-10}$$

Reduce the fraction \frac{-335}{-10} to lowest terms by extracting and canceling out -5.

$$f_{1}=\frac{67}{2}$$