Question

11 analyze and persevere two rival dry cleaners both advertise their prices. let x equal the number of items dry cleaned. store a’s prices are represented by the expression 15x - 2. store b’s prices are represented by the expression 3(5x + 7). when do the two stores charge the same rate? explain.

Explanation:

Step1: Set the two expressions equal

$15x - 2=3(5x + 7)$

Step2: Expand the right - hand side

$15x - 2 = 15x+21$

Step3: Subtract $15x$ from both sides

$15x-15x - 2=15x - 15x+21$
$- 2=21$

Since $-2
eq21$, there is no solution. The two stores never charge the same rate.

Answer:

There is no value of $x$ for which the two stores charge the same rate because the resulting equation $-2 = 21$ is a false statement.