Trigonometry Examples

$\sqrt{- 6 x + 19} = x - 2$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $x$ from both sides of the equation.

$\sqrt{- 6 x + 19} - x = - 2$

Step 1.2

Add $2$ to both sides of the equation.

$\sqrt{- 6 x + 19} - x + 2 = 0$

Step 2

Set the radicand in $\sqrt{- 6 x + 19}$ less than $0$ to find where the expression is undefined.

$- 6 x + 19 < 0$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $19$ from both sides of the inequality.

$- 6 x < - 19$

Step 3.2

Divide each term in $- 6 x < - 19$ by $- 6$ and simplify.

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Step 3.2.1

Divide each term in $- 6 x < - 19$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} > \frac{- 19}{- 6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} > \frac{- 19}{- 6}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 19}{- 6}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Dividing two negative values results in a positive value.

$x > \frac{19}{6}$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x > \frac{19}{6}$

$(\frac{19}{6}, \infty)$

Step 5