Question

reasoning each month, a shopkeeper spends 5x + 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 \(5x + 17\) dollars, and the rent is \(3x-4\) dollars. So the cost for electricity \(E=(5x + 17)-(3x - 4)\).
Simplify the expression:

$$
LATEXBLOCK0
$$

Step2: Solve the inequality for \(x\)

We want to find when \(2x + 21<100\).
Subtract 21 from both sides of the inequality: \(2x+21-21<100 - 21\), which gives \(2x<79\).
Divide both sides by 2: \(x <\frac{79}{2}=39.5\)

Answer:

The shopkeeper spends \((2x + 21)\) dollars on electricity. The values of \(x\) for which he spends less than \(\$100\) on electricity are \(x<39.5\) (since \(x\) represents an amount of money, \(x>0\) in a practical sense, but from the inequality \(2x + 21<100\) we get \(x<39.5\))