91Ó°ÊÓ

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 $≤\text{or}â‰\yen$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b≤c⇒bÂ\pm a≤cÂ\pm a \\ 2.b≤c⇒ab≤ac,\text{if}a>0 \\ 3.b≤c⇒abâ‰\yen ac,\text{if}a<0 \end{gathered}$$

Let m represents how much money she can spend that month after buying a concert ticket.

The inequality:

$m+45≤60$

Solve for m:

$$\begin{gathered} m+45≤60 \\ m+45−45≤60−45 \\ m≤15 \end{gathered}$$

Lupe can spend that month after buying a concert ticket no more than $15.

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 $≤\text{or}â‰\yen$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b≤c⇒bÂ\pm a≤cÂ\pm a \\ 2.b≤c⇒ab≤ac,\text{if}a>0 \\ 3.b≤c⇒abâ‰\yen ac,\text{if}a<0 \end{gathered}$$

Let m represents how much money she can spend both these purchases and the concert ticket.

The inequality:

$m+45+9.99+2≤60$

Solve for m:

$$\begin{gathered} m+45+9.99+2≤60 \\ m+56.99≤60 \\ m+56.99−56.99≤60−56.99 \\ m≤3.01 \end{gathered}$$

Thus, Lupe can spend no more than $3.01 for both these purchases and the concert ticket.