Algebra Examples

$g (x) = 9 + \frac{5}{4} x$ $h (x) = 10 x - 28$

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (10 x - 28)$ by substituting in the value of $h$ into $g$ .

$g (10 x - 28) = 9 + \frac{5}{4} \cdot (10 x - 28)$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (10 x - 28) = 9 + \frac{5}{4} \cdot (10 x) + \frac{5}{4} \cdot - 28$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$g (10 x - 28) = 9 + \frac{5}{2 (2)} \cdot (10 x) + \frac{5}{4} \cdot - 28$

Step 3.2.2

Factor $2$ out of $10 x$ .

$g (10 x - 28) = 9 + \frac{5}{2 (2)} \cdot (2 (5 x)) + \frac{5}{4} \cdot - 28$

Step 3.2.3

Cancel the common factor.

$g (10 x - 28) = 9 + \frac{5}{2 \cdot 2} \cdot (2 (5 x)) + \frac{5}{4} \cdot - 28$

Step 3.2.4

Rewrite the expression.

$g (10 x - 28) = 9 + \frac{5}{2} \cdot (5 x) + \frac{5}{4} \cdot - 28$

Step 3.3

Combine $5$ and $\frac{5}{2}$ .

$g (10 x - 28) = 9 + \frac{5 \cdot 5}{2} x + \frac{5}{4} \cdot - 28$

Step 3.4

Multiply $5$ by $5$ .

$g (10 x - 28) = 9 + \frac{25}{2} x + \frac{5}{4} \cdot - 28$

Step 3.5

Combine $\frac{25}{2}$ and $x$ .

$g (10 x - 28) = 9 + \frac{25 x}{2} + \frac{5}{4} \cdot - 28$

Step 3.6

Cancel the common factor of $4$ .

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Step 3.6.1

Factor $4$ out of $- 28$ .

$g (10 x - 28) = 9 + \frac{25 x}{2} + \frac{5}{4} \cdot (4 (- 7))$

Step 3.6.2

Cancel the common factor.

$g (10 x - 28) = 9 + \frac{25 x}{2} + \frac{5}{4} \cdot (4 \cdot - 7)$

Step 3.6.3

Rewrite the expression.

$g (10 x - 28) = 9 + \frac{25 x}{2} + 5 \cdot - 7$

Step 3.7

Multiply $5$ by $- 7$ .

$g (10 x - 28) = 9 + \frac{25 x}{2} - 35$

Step 4

Subtract $35$ from $9$ .

$g (10 x - 28) = \frac{25 x}{2} - 26$