Algebra Examples

$49^{\frac{x}{4} - 1} = 343^{\frac{x}{3}}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$7^{2 (\frac{x}{4} - 1)} = 7^{3 \frac{x}{3}}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

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

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (\frac{x}{4} - 1)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 2 (\frac{x}{4} - 1) = 3 (\frac{x}{3})$

Step 3.1.2

Simplify by adding zeros.

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

Step 3.1.3

Apply the distributive property.

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

Step 3.1.4

Cancel the common factor of $2$ .

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Step 3.1.4.1

Factor $2$ out of $4$ .

$2 \frac{x}{2 (2)} + 2 \cdot - 1 = 3 (\frac{x}{3})$

Step 3.1.4.2

Cancel the common factor.

$2 \frac{x}{2 \cdot 2} + 2 \cdot - 1 = 3 (\frac{x}{3})$

Step 3.1.4.3

Rewrite the expression.

$\frac{x}{2} + 2 \cdot - 1 = 3 (\frac{x}{3})$

Step 3.1.5

Multiply $2$ by $- 1$ .

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

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\frac{x}{2} - 2 = x$

Step 3.3

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

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Step 3.3.1

Subtract $x$ from both sides of the equation.

$\frac{x}{2} - 2 - x = 0$

Step 3.3.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} - x \cdot \frac{2}{2} - 2 = 0$

Step 3.3.3

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

$\frac{x}{2} + \frac{- x \cdot 2}{2} - 2 = 0$

Step 3.3.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{2} - 2 = 0$

Step 3.3.5

Simplify each term.

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Step 3.3.5.1

Simplify the numerator.

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Step 3.3.5.1.1

Factor $x$ out of $x - x \cdot 2$ .

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Step 3.3.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{2} - 2 = 0$

Step 3.3.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{2} - 2 = 0$

Step 3.3.5.1.1.3

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{2} - 2 = 0$

Step 3.3.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 2)$ .

$\frac{x (1 - 1 \cdot 2)}{2} - 2 = 0$

Step 3.3.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{2} - 2 = 0$

Step 3.3.5.1.3

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{2} - 2 = 0$

Step 3.3.5.2

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} - 2 = 0$

Step 3.3.5.3

Move the negative in front of the fraction.

$- \frac{x}{2} - 2 = 0$

Step 3.4

Add $2$ to both sides of the equation.

$- \frac{x}{2} = 2$

Step 3.5

Multiply both sides of the equation by $- 2$ .

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

Step 3.6

Simplify both sides of the equation.

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Step 3.6.1

Simplify the left side.

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Step 3.6.1.1

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

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Step 3.6.1.1.1

Cancel the common factor of $2$ .

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Step 3.6.1.1.1.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 \cdot 2$

Step 3.6.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 3.6.1.1.1.3

Cancel the common factor.

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

Step 3.6.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot 2$

Step 3.6.1.1.2

Multiply.

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Step 3.6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 2$

Step 3.6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot 2$

Step 3.6.2

Simplify the right side.

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Step 3.6.2.1

Multiply $- 2$ by $2$ .

$x = - 4$