Finite Math Examples

$- 7 = - \frac{3}{4} \cdot \frac{5}{3} + \frac{23}{4}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Add $\frac{3}{4} \cdot \frac{5}{3}$ to both sides of the equation.

$- 7 + \frac{3}{4} \cdot \frac{5}{3} = \frac{23}{4}$

Step 1.2

Subtract $\frac{23}{4}$ from both sides of the equation.

$- 7 + \frac{3}{4} \cdot \frac{5}{3} - \frac{23}{4} = 0$

Step 2

Simplify $- 7 + \frac{3}{4} \cdot \frac{5}{3} - \frac{23}{4}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$- 7 + \frac{3}{4} \cdot \frac{5}{3} - \frac{23}{4} = 0$

Step 2.1.1.2

Rewrite the expression.

$- 7 + \frac{1}{4} \cdot 5 - \frac{23}{4} = 0$

Step 2.1.2

Combine $\frac{1}{4}$ and $5$ .

$- 7 + \frac{5}{4} - \frac{23}{4} = 0$

Step 2.2

Combine the numerators over the common denominator.

$- 7 + \frac{5 - 23}{4} = 0$

Step 2.3

Subtract $23$ from $5$ .

$- 7 + \frac{- 18}{4} = 0$

Step 2.4

Simplify each term.

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Step 2.4.1

Cancel the common factor of $- 18$ and $4$ .

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Step 2.4.1.1

Factor $2$ out of $- 18$ .

$- 7 + \frac{2 (- 9)}{4} = 0$

Step 2.4.1.2

Cancel the common factors.

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Step 2.4.1.2.1

Factor $2$ out of $4$ .

$- 7 + \frac{2 \cdot - 9}{2 \cdot 2} = 0$

Step 2.4.1.2.2

Cancel the common factor.

$- 7 + \frac{2 \cdot - 9}{2 \cdot 2} = 0$

Step 2.4.1.2.3

Rewrite the expression.

$- 7 + \frac{- 9}{2} = 0$

Step 2.4.2

Move the negative in front of the fraction.

$- 7 - \frac{9}{2} = 0$

Step 2.5

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 7 \cdot \frac{2}{2} - \frac{9}{2} = 0$

Step 2.6

Combine $- 7$ and $\frac{2}{2}$ .

$\frac{- 7 \cdot 2}{2} - \frac{9}{2} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 2 - 9}{2} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $- 7$ by $2$ .

$\frac{- 14 - 9}{2} = 0$

Step 2.8.2

Subtract $9$ from $- 14$ .

$\frac{- 23}{2} = 0$

Step 2.9

Move the negative in front of the fraction.

$- \frac{23}{2} = 0$

Step 3

Set the numerator equal to zero.

$23 = 0$

Step 4

Since $23 \neq 0$ , there are no solutions.

No solution