Algebra Examples

$10 = \frac{1 + 7 x}{7 + x}$

Step 1

Rewrite the equation as $\frac{1 + 7 x}{7 + x} = 10$ .

$\frac{1 + 7 x}{7 + x} = 10$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$7 + x, 1$

Step 2.2

Remove parentheses.

$7 + x, 1$

Step 2.3

The LCM of one and any expression is the expression.

$7 + x$

Step 3

Multiply each term in $\frac{1 + 7 x}{7 + x} = 10$ by $7 + x$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{1 + 7 x}{7 + x} = 10$ by $7 + x$ .

$\frac{1 + 7 x}{7 + x} (7 + x) = 10 (7 + x)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $7 + x$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{1 + 7 x}{7 + x} (7 + x) = 10 (7 + x)$

Step 3.2.1.2

Rewrite the expression.

$1 + 7 x = 10 (7 + x)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$1 + 7 x = 10 \cdot 7 + 10 x$

Step 3.3.2

Multiply $10$ by $7$ .

$1 + 7 x = 70 + 10 x$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 4.1.1

Subtract $10 x$ from both sides of the equation.

$1 + 7 x - 10 x = 70$

Step 4.1.2

Subtract $10 x$ from $7 x$ .

$1 - 3 x = 70$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $1$ from both sides of the equation.

$- 3 x = 70 - 1$

Step 4.2.2

Subtract $1$ from $70$ .

$- 3 x = 69$

Step 4.3

Divide each term in $- 3 x = 69$ by $- 3$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $- 3 x = 69$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{69}{- 3}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{69}{- 3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{69}{- 3}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $69$ by $- 3$ .

$x = - 23$