Question

reasoning each month, a shopkeeper spends 9x + 14 dollars on rent and electricity. if she spends 7x - 5 dollars on rent, how much does she 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). she spends dollars on electricity. (simplify your answer)

Explanation:

Step1: Set up the equation for electricity cost

Let \(E\) be the cost of electricity. We know that total cost (rent + electricity) \(T=9x + 14\) and rent cost \(R = 7x-5\). Using the formula \(T=R + E\), we can solve for \(E\): \(E=T - R\).
Substitute \(T = 9x+14\) and \(R=7x - 5\) into the formula: \(E=(9x + 14)-(7x - 5)\).

Step2: Simplify the expression for \(E\)

Use the distributive property \(a-(b - c)=a - b + c\). So, \(E=9x+14 - 7x + 5\).
Combine like - terms: \((9x-7x)+(14 + 5)=2x+19\).

Answer:

\(2x + 19\)