Question

understand and write inequalities
quick review
an inequality is a mathematical sentence that contains < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or a first - equal - to!
examples
situation inequality
the age of the house, a, is greater than 8 years. a > 8
the cost of the house, c, is at least $85,000. c ≥ 85,000
the number of windows, w, is fewer than 10. w < 10
the number of people, p, living in the house is at most 5. p ≤ 5
the number of trucks, t, in the garage is not 2. t ≠ 2
exercises
write an inequality for each situation.

1. let h be a person’s height (in inches).
2. the value, v, of the find is less than $15.
3. the number of guests, g, coming for dinner is not 8.
4. the distance of the road, d, is at least 6 miles.
5. the time it takes to get to grandmother’s house, t, is longer than 2 hours.

lesson 4 - 2 solve inequalities
quick review
to graph the solutions of an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥. if the values of the variable are less than the given number, shade to the left on the number line. if the values of the variable are greater than the given number, shade to the right on the number line.
example
“molly is less than 15 years old” is represented by the inequality x < 15. write three ages that could represent molly’s age.
to graph the inequality on a number line, draw an open circle at 15 and shade to the left of 15 because x is less than 15. draw an arrow to show all numbers less than 15.
there are many solutions. molly could be 10, 12, 14, or any age less than 15 years.
exercises
write the inequality that each graph represents.

1. number line with 5,6,7,8,9,10,11,12,13,14,15
2. number line with 0,1,2,3,4,5,6,7,8,9,10
3. number line with 0,1,2,3,4,5,6,7,8,9,10
4. number line with 0,1,2,3,4,5,6,7,8,9,10

Explanation:

Step1: Analyze the first graph (Problem 1)

The number line has an open circle at 10 and shading to the left. An open circle means \( < \) or \( > \), and shading left means values less than 10. So the inequality is \( x < 10 \).

Step2: Analyze the second graph (Problem 2)

The number line has an open circle at 5 and shading to the right. Open circle and right shading mean values greater than 5, so \( x > 5 \).

Step3: Analyze the third graph (Problem 3)

The number line has a closed circle at 3 and shading to the right. Closed circle means \( \leq \) or \( \geq \), right shading means greater than or equal to 3, so \( x \geq 3 \).

Step4: Analyze the fourth graph (Problem 4)

The number line has a closed circle at 7 and shading to the left. Closed circle and left shading mean less than or equal to 7, so \( x \leq 7 \).

Answer:

1. \( x < 10 \)
2. \( x > 5 \)
3. \( x \geq 3 \)
4. \( x \leq 7 \)