Question

find the solution set for the following inequalities. for #7 and #8, find and graph the solution set.

1. ( 11 < -k + 19 )
2. ( 4k + 15 geq 50.88 )
3. ( \frac{3}{8}x + 14 leq 17 )
4. ( 5d - 19.8 < 18.7 ) (with number line)
5. ( 36 - 9x leq 62 ) (with number line)
6. what is the smallest value of ( x ) that is not a solution to ( 4x - 26 < 4 )?
7. rashaj has $37.25 in his wallet. he would like to purchase a movie ticket and some candy. the ticket costs $7.25 and each box of candy costs $3.75. he claims he can buy 5 boxes. do you agree or disagree? write and solve the inequality to explain your reasoning.
8. mason’s pet leopard gecko must be kept in a cage with a temperature of at least ( 82^circ\text{f} ). using the inequality ( \frac{9}{5}c + 32 geq 82 ), solve for ( c ) to determine the safe range of temperatures for his gecko in degrees celsius.
9. glenn has $1,250 in his savings account. in order to avoid bank fees, glenn must keep a minimum of $150 in his account. his cell phone costs him $35 per month. use an inequality to determine how many months glenn can pay for his cell phone before he would incur fees.

Explanation:

Let's solve question 7: \( 5d - 19.8 < 18.7 \)

Step 1: Add 19.8 to both sides

To isolate the term with \( d \), we add 19.8 to both sides of the inequality.
\( 5d - 19.8 + 19.8 < 18.7 + 19.8 \)
\( 5d < 38.5 \)

Step 2: Divide both sides by 5

To solve for \( d \), we divide both sides of the inequality by 5.
\( \frac{5d}{5} < \frac{38.5}{5} \)
\( d < 7.7 \)

Answer:

The solution set is \( d < 7.7 \). To graph this, we draw a number line, place an open circle at 7.7 (since \( d \) is less than 7.7, not less than or equal to), and shade the region to the left of 7.7.