Question

40 aubrey has $20 to spend on party supplies. she buys balloons for $16. the table shows prices for other items at the store. use the inequality ( a + 16 leq 20 ) to find which items aubrey can buy.
41 if ( a ) is equal to 4, ( a + 16 ) will be equal to 20.
if ( a ) is less than 4, ( a + 16 ) will be
less than 20.
42 graph an inequality to represent all possible values of ( a ).
number line from -5 to 15

Explanation:

Step1: Solve the inequality for $x$

Start with the given inequality:
$$x + 16 \leq 20$$
Subtract 16 from both sides:
$$x + 16 - 16 \leq 20 - 16$$
$$x \leq 4$$

Step2: Interpret the inequality for values

From $x \leq 4$, we confirm:

• When $x=4$, $4+16=20$
• When $x < 4$, $x+16 < 20$

Step3: Graph the inequality

On the number line:

1. Locate the point $4$.
2. Draw a closed (filled) circle at $4$ (since the inequality includes equality, $\leq$).
3. Draw a solid line extending to the left from $4$ to represent all values less than or equal to $4$.

Answer:

1. The completed statement: If $x$ is less than 4, $x + 16$ will be less than 20.
2. The solution to the inequality is $x \leq 4$. For the graph:

• Place a filled circle at 4 on the number line.
• Shade/draw a line to the left of 4, covering all values from 4 downwards.