Finite Math Examples

$\sqrt{7 - 3 x - 8}$

Step 1

Set the radicand in $\sqrt{7 - 3 x - 8}$ less than $0$ to find where the expression is undefined.

$7 - 3 x - 8 < 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $8$ from $7$ .

$- 3 x - 1 < 0$

Step 2.2

Add $1$ to both sides of the inequality.

$- 3 x < 1$

Step 2.3

Divide each term in $- 3 x < 1$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 x < 1$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{1}{- 3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{1}{- 3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{- 3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$x > - \frac{1}{3}$

Step 3

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 $0$ .

$x > - \frac{1}{3}$

$(- \frac{1}{3}, \infty)$

Step 4