Algebra Examples

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

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(- x + 1) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$2 x - 1 = - x \cdot 4 + 1 \cdot 4$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $4$ by $- 1$ .

$2 x - 1 = - 4 x + 1 \cdot 4$

Step 2.2.1.2.2

Multiply $4$ by $1$ .

$2 x - 1 = - 4 x + 4$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $4 x$ to both sides of the equation.

$2 x - 1 + 4 x = 4$

Step 3.1.2

Add $2 x$ and $4 x$ .

$6 x - 1 = 4$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$6 x = 4 + 1$

Step 3.2.2

Add $4$ and $1$ .

$6 x = 5$

Step 3.3

Divide each term in $6 x = 5$ by $6$ and simplify.

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Step 3.3.1

Divide each term in $6 x = 5$ by $6$ .

$\frac{6 x}{6} = \frac{5}{6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{5}{6}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{6}$

Decimal Form:

$x = 0.8\overline{3}$