Solve for x 17/3(x-3/2)=-5/4

$\frac{17}{3} (x - \frac{3}{2}) = - \frac{5}{4}$

Multiply both sides of the equation by $\frac{3}{17}$ .

$\frac{3}{17} (\frac{17}{3} \cdot (x - \frac{3}{2})) = \frac{3}{17} (- \frac{5}{4})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{17} (\frac{17}{3} \cdot (x - \frac{3}{2}))$ .

Apply the distributive property.

$\frac{3}{17} (\frac{17}{3} x + \frac{17}{3} (- \frac{3}{2})) = \frac{3}{17} (- \frac{5}{4})$

Combine $\frac{17}{3}$ and $x$ .

$\frac{3}{17} (\frac{17 x}{3} + \frac{17}{3} (- \frac{3}{2})) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{3}{17} (\frac{17 x}{3} + \frac{17}{3} \cdot \frac{- 3}{2}) = \frac{3}{17} (- \frac{5}{4})$

Factor $3$ out of $- 3$ .

$\frac{3}{17} (\frac{17 x}{3} + \frac{17}{3} \cdot \frac{3 (- 1)}{2}) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor.

$\frac{3}{17} (\frac{17 x}{3} + \frac{17}{3} \cdot \frac{3 \cdot - 1}{2}) = \frac{3}{17} (- \frac{5}{4})$

Rewrite the expression.

$\frac{3}{17} (\frac{17 x}{3} + 17 (\frac{- 1}{2})) = \frac{3}{17} (- \frac{5}{4})$

Combine $17$ and $\frac{- 1}{2}$ .

$\frac{3}{17} (\frac{17 x}{3} + \frac{17 \cdot - 1}{2}) = \frac{3}{17} (- \frac{5}{4})$

Simplify the expression.

Multiply $17$ by $- 1$ .

$\frac{3}{17} (\frac{17 x}{3} + \frac{- 17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Move the negative in front of the fraction.

$\frac{3}{17} (\frac{17 x}{3} - \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Apply the distributive property.

$\frac{3}{17} \cdot \frac{17 x}{3} + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{17} \cdot \frac{17 x}{3} + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Rewrite the expression.

$\frac{1}{17} (17 x) + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor of $17$ .

Factor $17$ out of $17 x$ .

$\frac{1}{17} (17 (x)) + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor.

$\frac{1}{17} (17 x) + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Rewrite the expression.

$x + \frac{3}{17} (- \frac{17}{2}) = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor of $17$ .

Move the leading negative in $- \frac{17}{2}$ into the numerator.

$x + \frac{3}{17} \cdot \frac{- 17}{2} = \frac{3}{17} (- \frac{5}{4})$

Factor $17$ out of $- 17$ .

$x + \frac{3}{17} \cdot \frac{17 (- 1)}{2} = \frac{3}{17} (- \frac{5}{4})$

Cancel the common factor.

$x + \frac{3}{17} \cdot \frac{17 \cdot - 1}{2} = \frac{3}{17} (- \frac{5}{4})$

Rewrite the expression.

$x + 3 (\frac{- 1}{2}) = \frac{3}{17} (- \frac{5}{4})$

Combine $3$ and $\frac{- 1}{2}$ .

$x + \frac{3 \cdot - 1}{2} = \frac{3}{17} (- \frac{5}{4})$

Simplify the expression.

Multiply $3$ by $- 1$ .

$x + \frac{- 3}{2} = \frac{3}{17} (- \frac{5}{4})$

Move the negative in front of the fraction.

$x - \frac{3}{2} = \frac{3}{17} (- \frac{5}{4})$

Simplify the right side.

Multiply $\frac{3}{17} (- \frac{5}{4})$ .

Multiply $\frac{3}{17}$ by $\frac{5}{4}$ .

$x - \frac{3}{2} = - \frac{3 \cdot 5}{17 \cdot 4}$

Multiply $3$ by $5$ .

$x - \frac{3}{2} = - \frac{15}{17 \cdot 4}$

Multiply $17$ by $4$ .

$x - \frac{3}{2} = - \frac{15}{68}$

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

Add $\frac{3}{2}$ to both sides of the equation.

$x = - \frac{15}{68} + \frac{3}{2}$

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{34}{34}$ .

$x = - \frac{15}{68} + \frac{3}{2} \cdot \frac{34}{34}$

Write each expression with a common denominator of $68$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{34}{34}$ .

$x = - \frac{15}{68} + \frac{3 \cdot 34}{2 \cdot 34}$

Multiply $2$ by $34$ .

$x = - \frac{15}{68} + \frac{3 \cdot 34}{68}$

Combine the numerators over the common denominator.

$x = \frac{- 15 + 3 \cdot 34}{68}$

Simplify the numerator.

Multiply $3$ by $34$ .

$x = \frac{- 15 + 102}{68}$

Add $- 15$ and $102$ .

$x = \frac{87}{68}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{87}{68}$

Decimal Form:

$x = 1.27941176 \dots$

Mixed Number Form:

$x = 1 \frac{19}{68}$

Solve for x 17/3(x-3/2)=-5/4

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