2.1 Homework: inequalities

• a Solve for $x$ .
• b Draw a number line, and show where the solution set to this problem is.
• c Pick an $x$ -value which, according to your drawing, is inside the solution set. Plug it into the original inequality . Does the inequality hold true?
• d Pick an $x$ -value which, according to your drawing, is outside the solution set. Plug it into the original inequality . Does the inequality hold true?

• a Solve for $x$ .
• b Draw a number line, and show where the solution set to this problem is.
• c Pick an $x$ -value which, according to your drawing, is inside the solution set. Plug it into the original inequality . Does the inequality hold true?
• d Pick an $x$ -value which, according to your drawing, is outside the solution set. Plug it into the original inequality . Does the inequality hold true?

• a Solve for $x$ .
• b Draw a number line, and show where the solution set to this problem is.
• c Pick an $x$ -value which, according to your drawing, is inside the solution set. Plug it into the original inequality . Does the inequality hold true?
• d Pick an $x$ -value which, according to your drawing, is outside the solution set. Plug it into the original inequality . Does the inequality hold true?

and . Draw a number line, and show where the solution set to this problem is.

or . Draw a number line, and show where the solution set to this problem is.

$x-\mathrm{2y}\ge 4$

• a Solve for $y$ .
• b Now—for the moment—let’s pretend that your equation said equals instead of “greater than” or “less than.” Then it would be the equation for a line. Find the slope and the y-intercept of that line, and graph it.
• Slope: _________
• y-intercept__________
• c Now, pick any point $(x,y)$ that is above that line. Plug the $x$ and $y$ coordinates into your inequality from part (a). Does this point fit the inequality? (Show your work…)
• d Now, pick any point $(x,y)$ that is below that line. Plug the $x$ and $y$ coordinates into your inequality from part (a). Does this point fit the inequality? (Show your work…)
• e So, is the solution to the inequality the points below or above the line? Shade the appropriate region on your graph.

Using a similar technique, draw the graph of $y\ge x^2$ . (If you don’t remember what the graph of $y\ge x^2$ looks like, try plotting a few points!)