Algebra Examples

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Simplify $(\frac{3}{7} x - 4) + 4 + \frac{5}{7} x - 4$ .

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Step 2.1

Combine the opposite terms in $(\frac{3}{7} x - 4) + 4 + \frac{5}{7} x - 4$ .

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Step 2.1.1

Add $- 4$ and $4$ .

$\frac{3}{7} x + 0 + \frac{5}{7} x - 4 = x$

Step 2.1.2

Add $\frac{3}{7} x$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Combine $\frac{3}{7}$ and $x$ .

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

Step 2.2.2

Combine $\frac{5}{7}$ and $x$ .

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

Step 2.3

Simplify terms.

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Step 2.3.1

Combine the numerators over the common denominator.

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

Step 2.3.2

Add $3 x$ and $5 x$ .

$- 4 + \frac{8 x}{7} = x$

Step 3

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

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Step 3.1

Subtract $x$ from both sides of the equation.

$- 4 + \frac{8 x}{7} - x = 0$

Step 3.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 4 + \frac{8 x}{7} - x \cdot \frac{7}{7} = 0$

Step 3.3

Combine $- x$ and $\frac{7}{7}$ .

$- 4 + \frac{8 x}{7} + \frac{- x \cdot 7}{7} = 0$

Step 3.4

Combine the numerators over the common denominator.

$- 4 + \frac{8 x - x \cdot 7}{7} = 0$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $8 x - x \cdot 7$ .

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Step 3.5.1.1.1

Factor $x$ out of $8 x$ .

$- 4 + \frac{x \cdot 8 - x \cdot 7}{7} = 0$

Step 3.5.1.1.2

Factor $x$ out of $- x \cdot 7$ .

$- 4 + \frac{x \cdot 8 + x (- 1 \cdot 7)}{7} = 0$

Step 3.5.1.1.3

Factor $x$ out of $x \cdot 8 + x (- 1 \cdot 7)$ .

$- 4 + \frac{x (8 - 1 \cdot 7)}{7} = 0$

Step 3.5.1.2

Multiply $- 1$ by $7$ .

$- 4 + \frac{x (8 - 7)}{7} = 0$

Step 3.5.1.3

Subtract $7$ from $8$ .

$- 4 + \frac{x \cdot 1}{7} = 0$

Step 3.5.2

Multiply $x$ by $1$ .

$- 4 + \frac{x}{7} = 0$

Step 4

Add $4$ to both sides of the equation.

$\frac{x}{7} = 4$

Step 5

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \cdot 4$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $7$ .

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Step 6.1.1.1

Cancel the common factor.

$7 \frac{x}{7} = 7 \cdot 4$

Step 6.1.1.2

Rewrite the expression.

$x = 7 \cdot 4$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $7$ by $4$ .

$x = 28$