Question

you need to help your family promote the taco truck to attract more customers.

your first step is to hire a graphic designer to create a fresh, new logo. the graphic designer provides their pricing structure and how it relates to your budget in the form of an equation:

(500 = 60(h - 1))

here, (h) represents the time the designer spends creating the logo. you need to find out how many hours of the designers work you can afford by solving the equation for (h).

your first step is shown below:

(500 = 60(h - 1))

(500 = 60h - 60)

which of the following describes your first step in solving the equation?

you simplify the right side of the equation by combining like terms.
you adjust the right side of the equation by using the distributive property.
you multiply both sides of the equation by a constant.
you divide both sides of the equation by a variable.

Explanation:

Analyze the given step

The original equation is:

$$500 = 60(h - 1)$$

The first step shown is:

$$500 = 60h - 60$$

Identify the algebraic property

To go from \(60(h - 1)\) to \(60h - 60\), the term \(60\) outside the parentheses is multiplied by each term inside the parentheses:

$$60 \cdot h = 60h$$

$$60 \cdot (-1) = -60$$

This operation is the application of the Distributive Property.

Evaluate the options

• Option 1: "You simplify the right side of the equation by combining like terms." — Incorrect, as \(h\) and \(-1\) are not like terms.
• Option 2: "You adjust the right side of the equation by using the distributive property." — Correct, as \(60\) is distributed to both \(h\) and \(-1\).
• Option 3: "You multiply both sides of the equation by a constant." — Incorrect, only the right side was expanded; the left side remained \(500\).
• Option 4: "You divide both sides of the equation by a variable." — Incorrect, no division occurred.

Answer:

• You simplify the right side of the equation by combining like terms.
• You adjust the right side of the equation by using the distributive property. (Correct answer)
• You multiply both sides of the equation by a constant.
• You divide both sides of the equation by a variable.