Question

tasha has a gift card to buy tickets to the movie theater. the initial value of the gift card is $120. the function m(x)=120 - 12x represents the amount of money, m, in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each. complete the statements. the solution to m(x)=180 is x = - 5 which in terms of the given context

Explanation:

Step1: Set up the equation

We are given the function $M(x)=120 - 12x$ and we want to find $x$ when $M(x)=180$. So we set up the equation $120-12x = 180$.

Step2: Isolate the variable - term

Subtract 120 from both sides of the equation: $-12x=180 - 120$, which simplifies to $-12x = 60$.

Step3: Solve for x

Divide both sides by - 12: $x=\frac{60}{-12}=- 5$.

Answer:

-5, which means that in the context of the problem, it would imply a non - realistic situation since we can't buy a negative number of movie tickets. Here, the negative value of $x$ indicates that the equation $M(x)=180$ is not valid within the real - world context of buying movie tickets because the amount of money left on the gift card cannot exceed the initial amount ($120$) when buying tickets at a positive cost per ticket.