Finite Math Examples

$5 = \frac{15 - 24 a}{6}$

Step 1

Rewrite the equation as $\frac{15 - 24 a}{6} = 5$ .

$\frac{15 - 24 a}{6} = 5$

Step 2

Cancel the common factor of $15 - 24 a$ and $6$ .

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Step 2.1

Factor $3$ out of $15$ .

$\frac{3 (5) - 24 a}{6} = 5$

Step 2.2

Factor $3$ out of $- 24 a$ .

$\frac{3 (5) + 3 (- 8 a)}{6} = 5$

Step 2.3

Factor $3$ out of $3 (5) + 3 (- 8 a)$ .

$\frac{3 (5 - 8 a)}{6} = 5$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $6$ .

$\frac{3 (5 - 8 a)}{3 \cdot 2} = 5$

Step 2.4.2

Cancel the common factor.

$\frac{3 (5 - 8 a)}{3 \cdot 2} = 5$

Step 2.4.3

Rewrite the expression.

$\frac{5 - 8 a}{2} = 5$

$\frac{5 - 8 a}{2} = 5$

$\frac{5 - 8 a}{2} = 5$

Step 3

Multiply both sides by $2$ .

$\frac{5 - 8 a}{2} \cdot 2 = 5 \cdot 2$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5 - 8 a}{2} \cdot 2$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5 - 8 a}{2} \cdot 2 = 5 \cdot 2$

Step 4.1.1.1.2

Rewrite the expression.

$5 - 8 a = 5 \cdot 2$

$5 - 8 a = 5 \cdot 2$

Step 4.1.1.2

Reorder $5$ and $- 8 a$ .

$- 8 a + 5 = 5 \cdot 2$

$- 8 a + 5 = 5 \cdot 2$

$- 8 a + 5 = 5 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $5$ by $2$ .

$- 8 a + 5 = 10$

$- 8 a + 5 = 10$

$- 8 a + 5 = 10$

Step 5

Solve for $a$ .

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Step 5.1

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

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Step 5.1.1

Subtract $5$ from both sides of the equation.

$- 8 a = 10 - 5$

Step 5.1.2

Subtract $5$ from $10$ .

$- 8 a = 5$

$- 8 a = 5$

Step 5.2

Divide each term in $- 8 a = 5$ by $- 8$ and simplify.

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Step 5.2.1

Divide each term in $- 8 a = 5$ by $- 8$ .

$\frac{- 8 a}{- 8} = \frac{5}{- 8}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 8$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 8 a}{- 8} = \frac{5}{- 8}$

Step 5.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{5}{- 8}$

$a = \frac{5}{- 8}$

$a = \frac{5}{- 8}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Move the negative in front of the fraction.

$a = - \frac{5}{8}$

$a = - \frac{5}{8}$

$a = - \frac{5}{8}$

$a = - \frac{5}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{5}{8}$

Decimal Form:

$a = - 0.625$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$