Algebra Examples

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

Step 1

Simplify $\frac{2 x + 6}{2} - x$ .

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Step 1.1

Cancel the common factor of $2 x + 6$ and $2$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

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

Step 1.1.2

Factor $2$ out of $6$ .

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

Step 1.1.3

Factor $2$ out of $2 (x) + 2 (3)$ .

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

Step 1.1.4

Cancel the common factors.

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Step 1.1.4.1

Factor $2$ out of $2$ .

$\frac{2 (x + 3)}{2 (1)} - x = 3$

Step 1.1.4.2

Cancel the common factor.

$\frac{2 (x + 3)}{2 \cdot 1} - x = 3$

Step 1.1.4.3

Rewrite the expression.

$\frac{x + 3}{1} - x = 3$

Step 1.1.4.4

Divide $x + 3$ by $1$ .

$x + 3 - x = 3$

$x + 3 - x = 3$

$x + 3 - x = 3$

Step 1.2

Combine the opposite terms in $x + 3 - x$ .

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Step 1.2.1

Subtract $x$ from $x$ .

$0 + 3 = 3$

Step 1.2.2

Add $0$ and $3$ .

$3 = 3$

$3 = 3$

$3 = 3$

Step 2

Since $3 = 3$ , the equation will always be true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$