Precalculus Examples

$a \cdot 19 = - 3 + (19 - 1) \cdot 5$

Step 1

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

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Step 1.1

Add $3$ to both sides of the equation.

$a \cdot 19 + 3 = (19 - 1) \cdot 5$

Step 1.2

Subtract $(19 - 1) \cdot 5$ from both sides of the equation.

$a \cdot 19 + 3 - (19 - 1) \cdot 5 = 0$

Step 2

Simplify $a \cdot 19 + 3 - (19 - 1) \cdot 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $19$ to the left of $a$ .

$19 \cdot a + 3 - (19 - 1) \cdot 5 = 0$

Step 2.1.2

Subtract $1$ from $19$ .

$19 a + 3 - 1 \cdot 18 \cdot 5 = 0$

Step 2.1.3

Multiply $- 1 \cdot 18 \cdot 5$ .

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Step 2.1.3.1

Multiply $- 1$ by $18$ .

$19 a + 3 - 18 \cdot 5 = 0$

Step 2.1.3.2

Multiply $- 18$ by $5$ .

$19 a + 3 - 90 = 0$

Step 2.2

Subtract $90$ from $3$ .

$19 a - 87 = 0$

Step 3

Add $87$ to both sides of the equation.

$19 a = 87$

Step 4

Divide each term in $19 a = 87$ by $19$ and simplify.

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Step 4.1

Divide each term in $19 a = 87$ by $19$ .

$\frac{19 a}{19} = \frac{87}{19}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $19$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{19 a}{19} = \frac{87}{19}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{87}{19}$