Question

algebra 1 semester review
equations, inequalities, linear functions, and systems
name

1. solve.

$-12 = \frac{2}{3}a + 6$
a. -27
b. -21
c. -18
d. -9

1. solve.

$-7(k + 5) = 3k - (8k - 1)$
a. -17
b. 17
c. -18
d. 18

1. solve.

$4x + 2 < 8x - (6x - 10)$
a. $x < -6.5$
b. $x > -6.5$
c. $x < 4$
d. $x > 4$

1. solve.

$3 - \frac{1}{2}x \leq 11$
a. $x \leq -4$
b. $x \geq -4$
c. $x \leq -16$
d. $x \geq -16$

1. the total cost (c) of renting a sailboat for n days is given by the inequality $c \geq 120 + 60n$. what is the maximum amount of days for which a sailboat can be rented if the total cost was $360?

a. 2 days
b. 4 days
c. 6 days
d. 8 days

1. identify the domain of the following relation:

${(3, -2), (0, 7), (2, -1), (4, 3)}$
a. {all real numbers}
b. {0,1,2,3,4}
c. {0,2,3,4}
d. {-1, -2,3,7}

1. what is the range of the relation plotted on the graph?

a. {-1,0,1,3}
b. {-2,0,1,3}
c. {-2 - 1,0,1,2,3}
d. {0,1,2,3}
(graph for question 7: a coordinate grid with plotted points)

1. what is the range of the graph below?

a. $-1 \leq x \leq 5$
b. $-2 \leq x \leq 4$
c. $-1 \leq y \leq 5$
d. $-2 \leq y \leq 4$
(graph for question 8: a circle on a coordinate grid)

Explanation:

Problem 1

Step1: Subtract 6 from both sides

$-12 - 6 = \frac{2}{3}a + 6 - 6$ → $-18 = \frac{2}{3}a$

Step2: Multiply by $\frac{3}{2}$

$-18 \times \frac{3}{2} = a$ → $a = -27$

Problem 2

Step1: Expand left side

$-7k - 35 = 3k - 8k + 1$

Step2: Simplify right side

$-7k - 35 = -5k + 1$

Step3: Rearrange terms

$-7k + 5k = 1 + 35$ → $-2k = 36$ → $k = -17$

Problem 3

Step1: Expand right side

$4x + 2 < 8x - 6x + 10$ → $4x + 2 < 2x + 10$

Step2: Rearrange terms

$4x - 2x < 10 - 2$ → $2x < 8$ → $x < 4$

Problem 4

Step1: Subtract 3 from both sides

$-\frac{1}{2}x ≤ 11 - 3$ → $-\frac{1}{2}x ≤ 8$

Step2: Multiply by -2 (reverse inequality)

$x ≥ -16$

Problem 5

Step1: Substitute c=360

$360 ≥ 120 + 60n$

Step2: Solve for n

$240 ≥ 60n$ → $n ≤ 4$ → max 4 days

Problem 6

Step1: Identify domain (x-values)

Relation: {(3,-2),(0,7),(2,-1),(4,3)} → x-values: 0,2,3,4

Problem 7

Step1: Identify range (y-values from graph)

Graph points have y-values: -2,0,1,3 → range: {-2,0,1,3}

Problem 8

Step1: Identify range (y-values of circle)

Circle spans y from -2 to 4 → $-2 ≤ y ≤ 4$

Answer:

1. A. -27
2. A. -17
3. C. x < 4
4. D. x ≥ -16
5. B. 4 days
6. C. {0,2,3,4}
7. B. {-2,0,1,3}
8. D. -2 ≤ y ≤ 4