Algebra Examples

$\frac{1}{2} (4 x - 10) + 5 = x - 11$

Step 1

Simplify $\frac{1}{2} \cdot (4 x - 10) + 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{2} (4 x) + \frac{1}{2} \cdot - 10 + 5 = x - 11$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $4 x$ .

$\frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 10 + 5 = x - 11$

Step 1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 10 + 5 = x - 11$

Step 1.1.2.3

Rewrite the expression.

$2 x + \frac{1}{2} \cdot - 10 + 5 = x - 11$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 10$ .

$2 x + \frac{1}{2} \cdot (2 (- 5)) + 5 = x - 11$

Step 1.1.3.2

Cancel the common factor.

$2 x + \frac{1}{2} \cdot (2 \cdot - 5) + 5 = x - 11$

Step 1.1.3.3

Rewrite the expression.

$2 x - 5 + 5 = x - 11$

Step 1.2

Combine the opposite terms in $2 x - 5 + 5$ .

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Step 1.2.1

Add $- 5$ and $5$ .

$2 x + 0 = x - 11$

Step 1.2.2

Add $2 x$ and $0$ .

$2 x = x - 11$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$2 x - x = - 11$

Step 2.2

Subtract $x$ from $2 x$ .

$x = - 11$