Question

reasoning each month, a shopkeeper spends 6x + 17 dollars on rent and electricity. if he spends 3x - 4 dollars on rent,
how much does he spend on electricity? use pencil and paper. for which value(s) of x is the amount the shopkeeper
spends on electricity less than $100? explain how you found the value(s).
he spends □ dollars on electricity.
(simplify your answer.)

Explanation:

Step1: Find the expression for electricity cost

The total cost for rent and electricity is \(6x + 17\) dollars, and the rent is \(3x-4\) dollars. The cost for electricity \(E\) is the total cost minus the rent cost. So, \(E=(6x + 17)-(3x - 4)\).
Using the distributive property \(a-(b - c)=a - b + c\), we get \(E = 6x+17-3x + 4\).
Combining like - terms (\(6x-3x\) and \(17 + 4\)), we have \(E=(6x-3x)+(17 + 4)=3x+21\).

Step2: Set up the inequality

We want to find when the electricity cost is less than \(100\). So, we set up the inequality \(3x + 21<100\).
Subtract \(21\) from both sides of the inequality: \(3x+21-21<100 - 21\), which simplifies to \(3x<79\).
Divide both sides by \(3\): \(x<\frac{79}{3}\approx26.33\).

Answer:

He spends \(3x + 21\) dollars on electricity. The amount he spends on electricity is less than \(100\) when \(x<\frac{79}{3}\approx26.33\). We found the electricity cost by subtracting the rent cost (\(3x - 4\)) from the total rent - electricity cost (\(6x + 17\)). Then we set up the inequality \(3x+21 < 100\) and solved for \(x\) using basic algebraic operations (subtraction and division).