Linear Algebra Examples

$x + 5 a - \sqrt{2 b} = 1$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $5 a$ from both sides of the equation.

$x - \sqrt{2 b} = 1 - 5 a$

Step 1.2

Add $\sqrt{2 b}$ to both sides of the equation.

$x = 1 - 5 a + \sqrt{2 b}$

Step 2

Set the radicand in $\sqrt{2 b}$ greater than or equal to $0$ to find where the expression is defined.

$2 b \geq 0$

Step 3

Divide each term in $2 b \geq 0$ by $2$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $2 b \geq 0$ by $2$ .

$\frac{2 b}{2} \geq \frac{0}{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 b}{2} \geq \frac{0}{2}$

Step 3.2.1.2

Divide $b$ by $1$ .

$b \geq \frac{0}{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $0$ by $2$ .

$b \geq 0$

Step 4

The domain is all values of $a$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${b | b \geq 0}$