Algebra Examples

$2 + \sqrt{2 x - 3} = \sqrt{x + 7}$

Step 1

Subtract $\sqrt{x + 7}$ from both sides of the equation.

$2 + \sqrt{2 x - 3} - \sqrt{x + 7} = 0$

Step 2

Set the radicand in $\sqrt{2 x - 3}$ less than $0$ to find where the expression is undefined.

$2 x - 3 < 0$

Step 3

Solve for $x$ .

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Step 3.1

Add $3$ to both sides of the inequality.

$2 x < 3$

Step 3.2

Divide each term in $2 x < 3$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x < 3$ by $2$ .

$\frac{2 x}{2} < \frac{3}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} < \frac{3}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{3}{2}$

Step 4

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

$x + 7 < 0$

Step 5

Subtract $7$ from both sides of the inequality.

$x < - 7$

Step 6

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 $0$ .

$x < \frac{3}{2}$

$(- \infty, \frac{3}{2})$

Step 7