End-of-Unit Assessment

Consider the inequality $\dfrac{x+3}6 > \dfrac {x}{4} +1$.

Which value of $x$ is a solution to the inequality?

The number of fish in a pond is eight more than the number of frogs. The total number of fish and frogs in the pond is at least 20. If $x$ represents the number of frogs, which inequality can be used to represent this situation?

Which graph represents the solution to this system of inequalities? $\begin {cases} 3x-5y \leq 15\\ y > \text- \frac 23 x+1 \end {cases}$

A graph of two intersecting inequalities on a coordinate plane, origin O. Horizontal x axis from negative 8 to 11, by 1's. Vertical y axis from negative 6 to 5, by 1's. Solid line starts at negative 5 comma negative 6, passes through 0 comma negative 3, 5 comma 0, and 10 comma 3. The region below the solid line is shaded. Dashed line starts above the x axis and to the left of the y axis, and passes through 0 comma 1, 3 comma negative 1, and 9 comma negative 5. The area below the dotted line is shaded.

A graph of two intersecting inequalities on a coordinate plane, origin O. Horizontal x axis from negative 8 to 11, by 1's. Vertical y axis from negative 6 to 5, by 1's. Solid line starts at negative 5 comma negative 6, passes through 0 comma negative 3, 5 comma 0, and 10 comma 3. The region above the solid line is shaded. Dashed line passes through 0 comma 1, 3 comma negative 1, and 9 comma negative 5. The area above the dotted line is shaded.

A graph of two intersecting inequalities on a coordinate plane, origin O. Horizontal x axis from negative 8 to 11, by 1's. Vertical y axis from negative 6 to 5, by 1's. Solid line starts at negative 5 comma negative 6, passes through 0 comma negative 3, 5 comma 0, and 10 comma 3. The region above the solid line is shaded. Dashed line starts above the x axis and to the left of the y axis, and passes through 0 comma 1, 3 comma negative 1, and 9 comma negative 5. The area above the dotted line is shaded.

A graph of two intersecting inequalities on a coordinate plane, origin O. Horizontal x axis from negative 8 to 11, by 1's. Vertical y axis from negative 6 to 5, by 1's. Solid line starts at negative 5 comma negative 6, passes through 0 comma negative 3, 5 comma 0, and 10 comma 3. The region above the solid line is shaded. Dashed line starts above the x axis and to the left of the y axis, and passes through 0 comma 1, 3 comma negative 1, and 9 comma negative 5. The area below the dotted line is shaded.

Graph the solution to the inequality $4x+5y<20$.

Blank x y coordinate plane with grid and origin labeled O. Both axes labeled from negative 6 to 5 by 1's.

A hairstylist charges $15 for an adult haircut and $9 for a child haircut. She wants to earn at least $360 dollars and cut a maximum of 30 haircuts this week. The graphs represent the hairstylist's constraints.

Two inequalities graphed on a coordinate plane, origin O, scale from 0 to 45 on both axes. Horizontal axis, number of adult haircuts. Vertical axis, number of child haircuts. A solid line starts on vertical axis at 40, goes through 15 comma 15 and ends on horizontal axis at 24. The region above the solid line is shaded. Another solid line starts on the vertical axis at 30, goes through 5 comma 25, 10 comma 20, 20 comma 10, and ends on the horizontal axis at 30. The region below the solid line is shaded.

List two points that could represent the numbers of adult and child haircuts that meet the hairstylist's goals.

A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each necklace is $4.50. The artist is selling the necklaces at $12 each.

The inequality $12n > 135 + 4.50n$ represents the situation in which the artist makes a profit.

1. Will the artist make a profit if she sells 15 necklaces? Show how you know.
2. Write an equivalent inequality with $n$ by itself on one side. Show your reasoning.

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.

1. Create a system of equations or inequalities that models the situation. Define the variables that you use.
2. The graph shows one of the relevant equations in this situation. Draw the graph of the other relevant equation.
   

   

   A blank coordinate grid with origin 0. Horizontal axis 0 to 24, by 2's. Vertical axis from 0 to 24, by 2's.

3. Show all the points that represent the number of hours the student can work at each job and meet his goal.

Which graph is the solution to the inequality $6.4 - 4x \geq -2.8$?

Graph the system of inequalities on the set of axes below:

$\begin{cases} y > 3x - 4 \\ x + 2y \leq 6 \end{cases}$

Label the solution set S.