Solve for r 68=3(6r-1)-7(1-3r)

$68 = 3 (6 r - 1) - 7 (1 - 3 r)$

Step 1

Rewrite the equation as $3 (6 r - 1) - 7 (1 - 3 r) = 68$ .

$3 (6 r - 1) - 7 (1 - 3 r) = 68$

Step 2

Simplify $3 (6 r - 1) - 7 (1 - 3 r)$ .

Simplify each term.

Apply the distributive property.

$3 (6 r) + 3 \cdot - 1 - 7 (1 - 3 r) = 68$

Multiply $6$ by $3$ .

$18 r + 3 \cdot - 1 - 7 (1 - 3 r) = 68$

Multiply $3$ by $- 1$ .

$18 r - 3 - 7 (1 - 3 r) = 68$

Apply the distributive property.

$18 r - 3 - 7 \cdot 1 - 7 (- 3 r) = 68$

Multiply $- 7$ by $1$ .

$18 r - 3 - 7 - 7 (- 3 r) = 68$

Multiply $- 3$ by $- 7$ .

$18 r - 3 - 7 + 21 r = 68$

Simplify by adding terms.

Add $18 r$ and $21 r$ .

$39 r - 3 - 7 = 68$

Subtract $7$ from $- 3$ .

$39 r - 10 = 68$

Step 3

Move all terms not containing $r$ to the right side of the equation.

Add $10$ to both sides of the equation.

$39 r = 68 + 10$

Add $68$ and $10$ .

$39 r = 78$

Step 4

Divide each term in $39 r = 78$ by $39$ and simplify.

Divide each term in $39 r = 78$ by $39$ .

$\frac{39 r}{39} = \frac{78}{39}$

Simplify the left side.

Cancel the common factor of $39$ .

Cancel the common factor.

$\frac{39 r}{39} = \frac{78}{39}$

Divide $r$ by $1$ .

$r = \frac{78}{39}$

Simplify the right side.

Divide $78$ by $39$ .

$r = 2$