Question

1 solve and graph.
$y - 9 - 4y < - 3$
a) $y < - 2$
b) $y > 4$
c) $y < 4$
d) $y > - 2$
2 for her cell phone plan, vicki pays $30 per
month plus $0.05 per text. she wants to
keep her bill under $60 per month. which
inequality represents the number of texts, $t$,
vicki can send each month while staying within
hcr budget?
a) $t > 600$
b) $t < 600$
c) $t < 1,800$
d) $t > 1,800$
3 rebecca buys some scarves that cost $6 each and
4 purses that cost $10 each. the cost of
rebeccas total purchase is $39. what equation
can be used to find the $n$, the number of scarves
that rebecca buys?
a) $6 + 40n = 39$
b) $6n + 40 = 39$
c) $(24 + 10)n = 39$
d) $18cdot4 + n = 39$

Explanation:

Step1: Solve the inequality \(y - 9-4y\leq - 3\)

Combine like - terms: \(y-4y-9\leq - 3\), which simplifies to \(-3y-9\leq - 3\).
Add 9 to both sides: \(-3y-9 + 9\leq - 3+9\), so \(-3y\leq6\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(y\geq - 2\).

Step2: Analyze the graph for the inequality \(y\geq - 2\)

The graph of \(y\geq - 2\) has an open circle at \(y = - 2\) (since the original inequality was strict when we divided by a negative number, but actually for \(-3y\leq6\) when dividing by \(-3\) we get \(y\geq - 2\), if we consider the graph of \(y>-2\) (the non - equality part of the solution from the options), it has an open circle at \(y=-2\) and the arrow points to the right.

Step3: Solve the cell - phone bill problem

The cost function \(C\) for Vicki's cell - phone bill is \(C = 30+0.05t\).
We want \(C<60\), so \(30 + 0.05t<60\).
Subtract 30 from both sides: \(0.05t<60 - 30\), so \(0.05t<30\).
Divide both sides by \(0.05\): \(t=\frac{30}{0.05}=600\), so \(t < 600\).

Step4: Solve the purchase problem

The cost of 4 purses at \(\$10\) each is \(4\times10 = 40\) dollars.
The cost of \(n\) scarves at \(\$6\) each is \(6n\) dollars.
The total cost is \(6n+40\), and since the total cost is \(\$39\) (assuming there is a typo and it should be \(6n + 40=39\) if we consider the structure of forming an equation from the problem description)

Answer:

1. D. \(y>-2\)
2. B. \(t < 600\)
3. B. \(6n + 40=39\)