Solve for x 2^7-3x=1/4

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

Step 1

Raise $2$ to the power of $7$ .

$128 - 3 x = \frac{1}{4}$

Step 2

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

Subtract $128$ from both sides of the equation.

$- 3 x = \frac{1}{4} - 128$

To write $- 128$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 3 x = \frac{1}{4} - 128 \cdot \frac{4}{4}$

Combine $- 128$ and $\frac{4}{4}$ .

$- 3 x = \frac{1}{4} + \frac{- 128 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- 3 x = \frac{1 - 128 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 128$ by $4$ .

$- 3 x = \frac{1 - 512}{4}$

Subtract $512$ from $1$ .

$- 3 x = \frac{- 511}{4}$

Move the negative in front of the fraction.

$- 3 x = - \frac{511}{4}$

Step 3

Divide each term in $- 3 x = - \frac{511}{4}$ by $- 3$ and simplify.

Divide each term in $- 3 x = - \frac{511}{4}$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- \frac{511}{4}}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- \frac{511}{4}}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- \frac{511}{4}}{- 3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{511}{4} \cdot \frac{1}{- 3}$

Move the negative in front of the fraction.

$x = - \frac{511}{4} (- \frac{1}{3})$

Multiply $- \frac{511}{4} (- \frac{1}{3})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{511}{4}) \frac{1}{3}$

Multiply $\frac{511}{4}$ by $1$ .

$x = \frac{511}{4} \cdot \frac{1}{3}$

Multiply $\frac{511}{4}$ by $\frac{1}{3}$ .

$x = \frac{511}{4 \cdot 3}$

Multiply $4$ by $3$ .

$x = \frac{511}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{511}{12}$

Decimal Form:

$x = 42.58\overline{3}$

Mixed Number Form:

$x = 42 \frac{7}{12}$

Solve for x 2^7-3x=1/4

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