Algebra Examples

$- 3 x + 3 (\frac{4}{3} x + 1) + \frac{1}{4} = 6$

Step 1

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

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $- 3 x$ as a fraction with denominator $1$ .

$\frac{- 3 x}{1} + 3 (\frac{4}{3} x + 1) + \frac{1}{4} = 6$

Step 1.1.2

Multiply $\frac{- 3 x}{1}$ by $\frac{4}{4}$ .

$\frac{- 3 x}{1} \cdot \frac{4}{4} + 3 (\frac{4}{3} x + 1) + \frac{1}{4} = 6$

Step 1.1.3

Multiply $\frac{- 3 x}{1}$ by $\frac{4}{4}$ .

$\frac{- 3 x \cdot 4}{4} + 3 (\frac{4}{3} x + 1) + \frac{1}{4} = 6$

Step 1.1.4

Write $3 (\frac{4}{3} x + 1)$ as a fraction with denominator $1$ .

$\frac{- 3 x \cdot 4}{4} + \frac{3 (\frac{4}{3} x + 1)}{1} + \frac{1}{4} = 6$

Step 1.1.5

Multiply $\frac{3 (\frac{4}{3} x + 1)}{1}$ by $\frac{4}{4}$ .

$\frac{- 3 x \cdot 4}{4} + \frac{3 (\frac{4}{3} x + 1)}{1} \cdot \frac{4}{4} + \frac{1}{4} = 6$

Step 1.1.6

Multiply $\frac{3 (\frac{4}{3} x + 1)}{1}$ by $\frac{4}{4}$ .

$\frac{- 3 x \cdot 4}{4} + \frac{3 (\frac{4}{3} x + 1) \cdot 4}{4} + \frac{1}{4} = 6$

Step 1.2

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 4 + 3 (\frac{4}{3} x + 1) \cdot 4 + 1}{4} = 6$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $4$ by $- 3$ .

$\frac{- 12 x + 3 (\frac{4}{3} x + 1) \cdot 4 + 1}{4} = 6$

Step 1.3.2

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

$\frac{- 12 x + 3 (\frac{4 x}{3} + 1) \cdot 4 + 1}{4} = 6$

Step 1.3.3

Apply the distributive property.

$\frac{- 12 x + (3 \frac{4 x}{3} + 3 \cdot 1) \cdot 4 + 1}{4} = 6$

Step 1.3.4

Cancel the common factor of $3$ .

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Step 1.3.4.1

Cancel the common factor.

$\frac{- 12 x + (3 \frac{4 x}{3} + 3 \cdot 1) \cdot 4 + 1}{4} = 6$

Step 1.3.4.2

Rewrite the expression.

$\frac{- 12 x + (4 x + 3 \cdot 1) \cdot 4 + 1}{4} = 6$

Step 1.3.5

Multiply $3$ by $1$ .

$\frac{- 12 x + (4 x + 3) \cdot 4 + 1}{4} = 6$

Step 1.3.6

Apply the distributive property.

$\frac{- 12 x + 4 x \cdot 4 + 3 \cdot 4 + 1}{4} = 6$

Step 1.3.7

Multiply $4$ by $4$ .

$\frac{- 12 x + 16 x + 3 \cdot 4 + 1}{4} = 6$

Step 1.3.8

Multiply $3$ by $4$ .

$\frac{- 12 x + 16 x + 12 + 1}{4} = 6$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Add $- 12 x$ and $16 x$ .

$\frac{4 x + 12 + 1}{4} = 6$

Step 1.4.2

Add $12$ and $1$ .

$\frac{4 x + 13}{4} = 6$

Step 2

Multiply both sides by $4$ .

$\frac{4 x + 13}{4} \cdot 4 = 6 \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{4 x + 13}{4} \cdot 4 = 6 \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$4 x + 13 = 6 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $6$ by $4$ .

$4 x + 13 = 24$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $13$ from both sides of the equation.

$4 x = 24 - 13$

Step 4.1.2

Subtract $13$ from $24$ .

$4 x = 11$

Step 4.2

Divide each term in $4 x = 11$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 x = 11$ by $4$ .

$\frac{4 x}{4} = \frac{11}{4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{11}{4}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{11}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{4}$

Decimal Form:

$x = 2.75$

Mixed Number Form:

$x = 2 \frac{3}{4}$