Solve for x (-3,-2) and (x,6) , m=2

$(- 3, - 2)$ and $(x, 6)$ , $m = 2$

Step 1

Slope $m$ is equal to the change in $y$ over the change in $x$ .

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 2

Substitute in the values of the known parameters.

$2 = \frac{6 - (- 2)}{x - (- 3)}$

Step 3

Solve for $x$ .

Rewrite the equation as $\frac{6 - (- 2)}{x - (- 3)} = 2$ .

$\frac{6 - (- 2)}{x - (- 3)} = 2$

Factor each term.

Multiply $- 1$ by $- 2$ .

$\frac{6 + 2}{x - (- 3)} = 2$

Add $6$ and $2$ .

$\frac{8}{x - (- 3)} = 2$

Multiply $- 1$ by $- 3$ .

$\frac{8}{x + 3} = 2$

Find the LCD of the terms in the equation.

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

$x + 3, 1$

Remove parentheses.

$x + 3, 1$

The LCM of one and any expression is the expression.

$x + 3$

Multiply each term in $\frac{8}{x + 3} = 2$ by $x + 3$ to eliminate the fractions.

Multiply each term in $\frac{8}{x + 3} = 2$ by $x + 3$ .

$\frac{8}{x + 3} (x + 3) = 2 (x + 3)$

Simplify the left side.

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{8}{x + 3} (x + 3) = 2 (x + 3)$

Rewrite the expression.

$8 = 2 (x + 3)$

Simplify the right side.

Apply the distributive property.

$8 = 2 x + 2 \cdot 3$

Multiply $2$ by $3$ .

$8 = 2 x + 6$

Solve the equation.

Rewrite the equation as $2 x + 6 = 8$ .

$2 x + 6 = 8$

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

Subtract $6$ from both sides of the equation.

$2 x = 8 - 6$

Subtract $6$ from $8$ .

$2 x = 2$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

Solve for x (-3,-2) and (x,6) , m=2

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