Finite Math Examples

$49 = a \cdot ((10 - 1) d)$ , $19 = a \cdot ((4 - 1) d)$

Step 1

Solve for $a$ in $49 = a \cdot (9 d)$ .

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Step 1.1

Rewrite the equation as $a \cdot (9 d) = 49$ .

$a \cdot (9 d) = 49$

$19 = a \cdot (3 d)$

Step 1.2

Divide each term in $a \cdot (9 d) = 49$ by $9 d$ and simplify.

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Step 1.2.1

Divide each term in $a \cdot (9 d) = 49$ by $9 d$ .

$\frac{a \cdot (9 d)}{9 d} = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $9$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{a \cdot (9 d)}{9 d} = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

Step 1.2.2.1.2

Rewrite the expression.

$\frac{a \cdot (d)}{d} = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

$\frac{a \cdot (d)}{d} = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

Step 1.2.2.2

Cancel the common factor of $d$ .

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Step 1.2.2.2.1

Cancel the common factor.

$\frac{a \cdot d}{d} = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

Step 1.2.2.2.2

Divide $a$ by $1$ .

$a = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

$a = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

$a = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

$a = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

$a = \frac{49}{9 d}$

$19 = a \cdot (3 d)$

Step 2

Replace all occurrences of $a$ with $\frac{49}{9 d}$ in each equation.

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Step 2.1

Replace all occurrences of $a$ in $19 = a \cdot (3 d)$ with $\frac{49}{9 d}$ .

$19 = (\frac{49}{9 d}) \cdot (3 d)$

$a = \frac{49}{9 d}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{49}{9 d}) \cdot (3 d)$ .

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$19 = 3 (\frac{49}{9 d}) \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $9 d$ .

$19 = 3 (\frac{49}{3 (3 d)}) \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.2.2

Cancel the common factor.

$19 = 3 (\frac{49}{3 (3 d)}) \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.2.3

Rewrite the expression.

$19 = \frac{49}{3 d} \cdot d$

$a = \frac{49}{9 d}$

$19 = \frac{49}{3 d} \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.3

Cancel the common factor of $d$ .

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Step 2.2.1.3.1

Factor $d$ out of $3 d$ .

$19 = \frac{49}{d \cdot 3} \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.3.2

Cancel the common factor.

$19 = \frac{49}{d \cdot 3} \cdot d$

$a = \frac{49}{9 d}$

Step 2.2.1.3.3

Rewrite the expression.

$19 = \frac{49}{3}$

$a = \frac{49}{9 d}$

$19 = \frac{49}{3}$

$a = \frac{49}{9 d}$

$19 = \frac{49}{3}$

$a = \frac{49}{9 d}$

$19 = \frac{49}{3}$

$a = \frac{49}{9 d}$

$19 = \frac{49}{3}$

$a = \frac{49}{9 d}$

Step 3

Since $19 = \frac{49}{3}$ is not true, there is no solution.

No solution