Solve 7(6+3t)+(-1/2)-2t-(-7/2-3t)=4

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

Solve for t

$$t = -\frac{41}{22} = -1\frac{19}{22} \approx -1.863636364$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 6+3t.

$$42+21t-\frac{1}{2}-2t-\left(-\frac{7}{2}-3t\right)=4$$

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

$$\frac{84}{2}+21t-\frac{1}{2}-2t-\left(-\frac{7}{2}-3t\right)=4$$

Since \frac{84}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{84-1}{2}+21t-2t-\left(-\frac{7}{2}-3t\right)=4$$

Subtract 1 from 84 to get 83.

$$\frac{83}{2}+21t-2t-\left(-\frac{7}{2}-3t\right)=4$$

Combine 21t and -2t to get 19t.

$$\frac{83}{2}+19t-\left(-\frac{7}{2}-3t\right)=4$$

To find the opposite of -\frac{7}{2}-3t, find the opposite of each term.

$$\frac{83}{2}+19t-\left(-\frac{7}{2}\right)-\left(-3t\right)=4$$

The opposite of -\frac{7}{2} is \frac{7}{2}.

$$\frac{83}{2}+19t+\frac{7}{2}-\left(-3t\right)=4$$

The opposite of -3t is 3t.

$$\frac{83}{2}+19t+\frac{7}{2}+3t=4$$

Since \frac{83}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{83+7}{2}+19t+3t=4$$

Add 83 and 7 to get 90.

$$\frac{90}{2}+19t+3t=4$$

Divide 90 by 2 to get 45.

$$45+19t+3t=4$$

Combine 19t and 3t to get 22t.

$$45+22t=4$$

Subtract 45 from both sides.

$$22t=4-45$$

Subtract 45 from 4 to get -41.

$$22t=-41$$

Divide both sides by 22.

$$t=\frac{-41}{22}$$

Fraction \frac{-41}{22} can be rewritten as -\frac{41}{22} by extracting the negative sign.

$$t=-\frac{41}{22}$$