Question

reasoning each month, a shopkeeper spends 7x + 15 dollars on rent and electricity. if he spends 5x - 2 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 \\(\square\\) dollars on electricity
(simplify your answer.)

Explanation:

Step1: Subtract rent from total cost

To find electricity cost, subtract rent expense from total rent+electricity expense:
$(7x + 19) - (5x - 2)$

Step2: Simplify the expression

Distribute the negative sign and combine like terms:
$7x + 19 - 5x + 2 = (7x-5x)+(19+2) = 2x + 21$

Step3: Set up inequality for <$100

We need electricity cost < 100, so:
$2x + 21 < 100$

Step4: Solve the inequality

Subtract 21 from both sides:
$2x < 100 - 21$
$2x < 79$
Divide by 2:
$x < \frac{79}{2}$
$x < 39.5$

Answer:

He spends $\boldsymbol{2x + 21}$ dollars on electricity.
The amount spent on electricity is less than $100 when $\boldsymbol{x < 39.5}$.