Q27. - Algebra 1

Question

Define a variable, write an inequality, and solve each problem. Check your solution. 

Shoe rental costs \(2, and each game bowled costs \)3. How many games can Kyle bowl without spending more than $15?

F. 2

G. 3

H. 4

J. 5

Step-by-Step Solution

Answer

The variable is x is and the inequality equation is $3x+2\le 15$. Kyle can bowl 4 games without spending more than $15.

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{ or }\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

width="189" style="max-width: none; vertical-align: -38px;" $$\begin{gathered} 1.b\le c\Rightarrow b\pm a\le c\pm a \\ \begin{array}{l}2.b\le c\Rightarrow ab\le ac,\text{ if }a>0\\ 3.b\le c\Rightarrow ab\ge ac,\text{ if }a<0\end{array} \end{gathered}$$

Step 2. Write the inequality for the given condition.

Let the number be x.

 Shoe rental costs $2, and each game bowled costs $3:

 $3x+2\le 15$

Step 3. Solve for x.

Solve for x  in the inequation $3x+2\le 15$

$$\begin{gathered} 3x+2\le 15 \\ 3x+2-2\le 15-2 \\ 3x\le 13 \\ \frac{3x}{3}\le \frac{13}{3} \\ x\le 4.33 \end{gathered}$$

Step 4. Check the solution .

Put the value of x as 3

$$\begin{gathered} 3x+2\le 15 \\ 3\left(3\right)+2\le 15 \\ 9+2\le 15 \\ 11\le 15 \left[\text{True Statement}\right] \end{gathered}$$ 

Thus, the solution of the inequality equation $3x+2\le 15$ is $x\le 4.33$.

Therefore, Kyle can bowl 4 games without spending more than $15.