Now You Try

<p>Define a variable, write an inequality, and solve each problem. Then check your
solution.</p><p>Negative seven times a number is at least 14.</p>

<p>Chemistry The pH level of a popular shampoo is between <code class='latex inline'>\displaystyle 6.0 </code> and <code class='latex inline'>\displaystyle 6.5 </code> inclusive. What compound inequality shows the pH levels of this shampoo? Graph the solution.</p>

<p>Construction A contractor estimated that her expenses for a construction project would be between <code class='latex inline'>\displaystyle \$ 700,000 </code> and <code class='latex inline'>\displaystyle \$ 750,000 </code>. She has already spent <code class='latex inline'>\displaystyle \$ 496,000 . </code> How much more can she spend and remain within her estimate?</p>

<p>Terrell has $65 to spend at the mall. He bought a T-shirt for $18 and a belt for $14. If Terrell still wants to buy a pair of jeans, how much can he spend on the jeans?</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your
solution.</p><p>Seven times a number is greater than 28.</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your solution.</p><p>Thirty is no greater than the sum of a number and -8.</p>

<p>The yearly membership to the San Diego Zoo for a family with 2 adults and 2 children is $144. The regular admission to the zoo is $18 for each adult and $8 for each child. How many times should such a family plan to visit the zoo in a year to make a membership less expensive than paying regular admission?</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your
solution.</p><p>Forty percent of a number is less than or equal to 45.</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your
solution.</p><p>Twenty-four is at most a third of a number.</p>

<p>The lengths of the sides of a triangle are in the ratio <code class='latex inline'>\displaystyle 5: 6: 7 </code>. Describe the length of the longest side if the perimeter is less than <code class='latex inline'>\displaystyle 54 \mathrm{~cm} . </code></p>

<p>The length of the base of the triangle at the right is less than the height of the triangle. What are the possible values of x?</p><img src="/qimages/24870" />

<p>Write the sentence as an inequality.
A number <code class='latex inline'>\displaystyle n </code> plus 7 is less than or equal to 9 .</p>

<p>In a factory, there are 10 assembly points equally spaced along a 9-m section of an assembly line. A supply bin is to be located 5 m away from the assembly line. Where is the best location for the supply bin so that the workers will have to go the least distance to get their supplies? Justify your solution.</p>

<p>Adult Nile crocodiles weigh up to 2200 pounds. If a young Nile crocodile weighs 157 pounds, how many pounds might it be expected to gain in its lifetime?</p>

<p>You save <code class='latex inline'>\displaystyle \$ 15 </code> per week to purchase one of the bikes shown. </p><p>a. Write and solve an inequality to find the numbers of weeks you need to save to purchase a bike.</p><p>b. Your parents give you <code class='latex inline'>\displaystyle \$ 65 </code> to help you buy the new bike. How does this affect you answer in part (a)? Use an inequality to justify your answer.</p><img src="/qimages/111037" />

<p>Three requirements for a lifeguard training course are shown. (Section 2.1)</p><p>a. Write and graph three inequalities that represent the requirements.</p><p>b. You can swim 250 feet, tread water for 6 minutes, and swim 35 feet underwater without taking a breath. Do you satisfy the requirements of the course? Explain.</p><img src="/qimages/74689" />

<p>Determine whether each statement is always, sometimes, or never true.</p><p>a. If <code class='latex inline'>a< b</code> and <code class='latex inline'>c< d</code>, then <code class='latex inline'>a+c< b+d</code>.</p><p>b. If <code class='latex inline'>a< b</code> and <code class='latex inline'>c< d</code>, then <code class='latex inline'>a+c\geq b+d</code>.</p><p>c. If <code class='latex inline'>a< b</code> and <code class='latex inline'>c< d</code>, then <code class='latex inline'>a-c=b-d</code>.</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your
solution.</p><p>Two thirds of a number is less than -15.</p>

<p>Write the sentence as an inequality.</p><p>A number <code class='latex inline'> x </code> is greater than 3 .</p>

<p>Define a variable, write an inequality, and solve each problem. Then check your solution.</p><p>Twice a number is more than the sum of that number and 14.</p>

<p>Banquet hall charges according to the equation <code>$40n-C+250=0$.</code></p>
<ul>
<li>Identify the fixed and variable costs.</li>
</ul>

<p>The Jefferson Band Boosters raised more than <code class='latex inline'>\displaystyle \$ 5500 </code> from sales of their <code class='latex inline'>\displaystyle \$ 15 </code> band DVD. Define a variable, and write an inequality to represent the number of DVDs they sold. Solve the inequality and interpret your solution.</p>

<p>Geometry The sum of the lengths of any two sides of a triangle is greater than the length of the third side. In <code class='latex inline'>\displaystyle \triangle A B C, B C=4 </code> and <code class='latex inline'>\displaystyle A C=8-A B </code>. What can you conclude about <code class='latex inline'>\displaystyle A B ? </code></p>

<p>The art department at a school sold 323 tickets to an art show, for a total of$790. Students paid $2 for tickets, and non-students paid $3.50. The principal asked how many non-students attended the art show.</p><p>a) Write a system of two linear equations for this situation.</p><p>b) Solve the problem by graphing the system.</p>