Algebra Examples

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

Step 1

Simplify $- \frac{1}{4} x - 4 + \frac{3}{4} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{1}{4}$ .

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

Step 1.1.2

Combine $\frac{3}{4}$ and $x$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

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

Step 1.2.2

Add $- x$ and $3 x$ .

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

Step 1.2.3

Cancel the common factor of $2$ and $4$ .

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Step 1.2.3.1

Factor $2$ out of $2 x$ .

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

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $4$ .

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

Step 1.2.3.2.2

Cancel the common factor.

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

Step 1.2.3.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{x}{2}$ from both sides of the equation.

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

Step 3.2

Combine the opposite terms in $- 4 + \frac{x}{2} - \frac{x}{2}$ .

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Step 3.2.1

Subtract $\frac{x}{2}$ from $\frac{x}{2}$ .

$- 4 + 0 = 1$

Step 3.2.2

Add $- 4$ and $0$ .

$- 4 = 1$

Step 4

Since $- 4 \neq 1$ , there are no solutions.

No solution