Precalculus Examples

$g (x) = 2 x - 5$ , $h (x) = 4 x + 5$ , $g (3) - h \cdot 3$

Step 1

Replace the variable $x$ with $3$ in the expression.

$g (3) = 2 (3) - 5$

Step 2

Replace the function designators in $g (3) - h \cdot 3$ with the actual functions.

$(2 (3) - 5) - (4 x + 5) \cdot 3$

Step 3

Simplify $(2 (3) - 5) - (4 x + 5) \cdot 3$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $3$ .

$6 - 5 - (4 x + 5) \cdot 3$

Step 3.1.2

Apply the distributive property.

$6 - 5 + (- (4 x) - 1 \cdot 5) \cdot 3$

Step 3.1.3

Multiply $4$ by $- 1$ .

$6 - 5 + (- 4 x - 1 \cdot 5) \cdot 3$

Step 3.1.4

Multiply $- 1$ by $5$ .

$6 - 5 + (- 4 x - 5) \cdot 3$

Step 3.1.5

Apply the distributive property.

$6 - 5 - 4 x \cdot 3 - 5 \cdot 3$

Step 3.1.6

Multiply $3$ by $- 4$ .

$6 - 5 - 12 x - 5 \cdot 3$

Step 3.1.7

Multiply $- 5$ by $3$ .

$6 - 5 - 12 x - 15$

Step 3.2

Simplify by subtracting numbers.

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Step 3.2.1

Subtract $5$ from $6$ .

$1 - 12 x - 15$

Step 3.2.2

Subtract $15$ from $1$ .

$- 12 x - 14$