Precalculus Examples

$7 y = - 8 e^{- x}$ , $y + 2 x + 23 = 0$

Step 1

Rewrite the equation as $- 8 e^{- x} = 7 (- 2 x - 23)$ .

$- 8 e^{- x} = 7 (- 2 x - 23)$

$y = - 2 x - 23$

Step 2

Simplify $7 (- 2 x - 23)$ .

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Step 2.1

Rewrite.

$- 8 e^{- x} = 0 + 0 + 7 (- 2 x - 23)$

$y = - 2 x - 23$

Step 2.2

Simplify by adding zeros.

$- 8 e^{- x} = 7 (- 2 x - 23)$

$y = - 2 x - 23$

Step 2.3

Apply the distributive property.

$- 8 e^{- x} = 7 (- 2 x) + 7 \cdot - 23$

$y = - 2 x - 23$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $- 2$ by $7$ .

$- 8 e^{- x} = - 14 x + 7 \cdot - 23$

$y = - 2 x - 23$

Step 2.4.2

Multiply $7$ by $- 23$ .

$- 8 e^{- x} = - 14 x - 161$

$y = - 2 x - 23$

$- 8 e^{- x} = - 14 x - 161$

$y = - 2 x - 23$

$- 8 e^{- x} = - 14 x - 161$

$y = - 2 x - 23$

Step 3

Add $8 e^{- x}$ to both sides of the equation.

$0 = - 14 x - 161 + 8 e^{- x}$

$y = - 2 x - 23$

Step 4

Rewrite the equation as $- 14 x - 161 + 8 e^{- x} = 0$ .

$- 14 x - 161 + 8 e^{- x} = 0$

$y = - 2 x - 23$