Algebra Examples

$\frac{1}{2} x - 4 + 1 = - 3 - \frac{1}{2} x$

Step 1

Simplify $\frac{1}{2} x - 4 + 1$ .

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Step 1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - 4 + 1 = - 3 - \frac{1}{2} x$

Step 1.2

Add $- 4$ and $1$ .

$\frac{x}{2} - 3 = - 3 - \frac{1}{2} x$

Step 2

Combine $x$ and $\frac{1}{2}$ .

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

Step 3

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

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Step 3.1

Add $\frac{x}{2}$ to both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Add $x$ and $x$ .

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Divide $x$ by $1$ .

$- 3 + x = - 3$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$x = - 3 + 3$

Step 4.2

Add $- 3$ and $3$ .

$x = 0$