Algebra Examples

$x - \frac{5 x + 2}{6} = \frac{7 - 3 x}{4}$

Step 1

Multiply both sides by $4$ .

$(x - \frac{5 x + 2}{6}) \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(x - \frac{5 x + 2}{6}) \cdot 4$ .

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Step 2.1.1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(x \cdot \frac{6}{6} - \frac{5 x + 2}{6}) \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Combine $x$ and $\frac{6}{6}$ .

$(\frac{x \cdot 6}{6} - \frac{5 x + 2}{6}) \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - (5 x + 2)}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Move $6$ to the left of $x$ .

$\frac{6 \cdot x - (5 x + 2)}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.3.2

Apply the distributive property.

$\frac{6 x - (5 x) - 1 \cdot 2}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.3.3

Multiply $5$ by $- 1$ .

$\frac{6 x - 5 x - 1 \cdot 2}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.3.4

Multiply $- 1$ by $2$ .

$\frac{6 x - 5 x - 2}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.3.5

Subtract $5 x$ from $6 x$ .

$\frac{x - 2}{6} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4

Simplify terms.

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Step 2.1.1.4.1

Cancel the common factor of $2$ .

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Step 2.1.1.4.1.1

Factor $2$ out of $6$ .

$\frac{x - 2}{2 (3)} \cdot 4 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4.1.2

Factor $2$ out of $4$ .

$\frac{x - 2}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4.1.3

Cancel the common factor.

$\frac{x - 2}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4.1.4

Rewrite the expression.

$\frac{x - 2}{3} \cdot 2 = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4.2

Combine $\frac{x - 2}{3}$ and $2$ .

$\frac{(x - 2) \cdot 2}{3} = \frac{7 - 3 x}{4} \cdot 4$

Step 2.1.1.4.3

Move $2$ to the left of $x - 2$ .

$\frac{2 (x - 2)}{3} = \frac{7 - 3 x}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{7 - 3 x}{4} \cdot 4$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{2 (x - 2)}{3} = \frac{7 - 3 x}{4} \cdot 4$

Step 2.2.1.1.2

Rewrite the expression.

$\frac{2 (x - 2)}{3} = 7 - 3 x$

Step 2.2.1.2

Reorder $7$ and $- 3 x$ .

$\frac{2 (x - 2)}{3} = - 3 x + 7$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $3$ .

$\frac{2 (x - 2)}{3} \cdot 3 = (- 3 x + 7) \cdot 3$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{2 (x - 2)}{3} \cdot 3$ .

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Step 3.2.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{2 (x - 2)}{3} \cdot 3 = (- 3 x + 7) \cdot 3$

Step 3.2.1.1.1.2

Rewrite the expression.

$2 (x - 2) = (- 3 x + 7) \cdot 3$

Step 3.2.1.1.2

Apply the distributive property.

$2 x + 2 \cdot - 2 = (- 3 x + 7) \cdot 3$

Step 3.2.1.1.3

Multiply $2$ by $- 2$ .

$2 x - 4 = (- 3 x + 7) \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(- 3 x + 7) \cdot 3$ .

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Step 3.2.2.1.1

Apply the distributive property.

$2 x - 4 = - 3 x \cdot 3 + 7 \cdot 3$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $3$ by $- 3$ .

$2 x - 4 = - 9 x + 7 \cdot 3$

Step 3.2.2.1.2.2

Multiply $7$ by $3$ .

$2 x - 4 = - 9 x + 21$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $9 x$ to both sides of the equation.

$2 x - 4 + 9 x = 21$

Step 3.3.1.2

Add $2 x$ and $9 x$ .

$11 x - 4 = 21$

Step 3.3.2

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

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Step 3.3.2.1

Add $4$ to both sides of the equation.

$11 x = 21 + 4$

Step 3.3.2.2

Add $21$ and $4$ .

$11 x = 25$

Step 3.3.3

Divide each term in $11 x = 25$ by $11$ and simplify.

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Step 3.3.3.1

Divide each term in $11 x = 25$ by $11$ .

$\frac{11 x}{11} = \frac{25}{11}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $11$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{11 x}{11} = \frac{25}{11}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{25}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{11}$

Decimal Form:

$x = 2.\overline{27}$

Mixed Number Form:

$x = 2 \frac{3}{11}$