Algebra Examples

$4 - (2 x + 5) = \frac{1}{2} (- 4 x - 2)$

Step 1

Simplify $4 - (2 x + 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 - (2 x) - 1 \cdot 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Step 1.1.2

Multiply $2$ by $- 1$ .

$4 - 2 x - 1 \cdot 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Step 1.1.3

Multiply $- 1$ by $5$ .

$4 - 2 x - 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Step 1.2

Subtract $5$ from $4$ .

$- 2 x - 1 = \frac{1}{2} \cdot (- 4 x - 2)$

Step 2

Simplify $\frac{1}{2} \cdot (- 4 x - 2)$ .

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Step 2.1

Apply the distributive property.

$- 2 x - 1 = \frac{1}{2} (- 4 x) + \frac{1}{2} \cdot - 2$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $- 4 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $- 2$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

$- 2 x - 1 = - 2 x - 1$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $2 x$ to both sides of the equation.

$- 2 x - 1 + 2 x = - 1$

Step 3.2

Combine the opposite terms in $- 2 x - 1 + 2 x$ .

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Step 3.2.1

Add $- 2 x$ and $2 x$ .

$0 - 1 = - 1$

Step 3.2.2

Subtract $1$ from $0$ .

$- 1 = - 1$

Step 4

Since $- 1 = - 1$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$