Unit 1 Review Math 1 Honors

Linear Equations

100

Solve for x:
x + 7 = 15

x = 8

200

Solve for y:
3y - 8 = 13

3y - 8 = 13

3y = 21

y = 7

300

Solve the following equation for x:
2x + 5 = 3x - 4

2x + 5 = 3x - 4

5 = x - 4

x = 9

400

Solve for a:
7(a + 2) = 7a + 26

7(a+2) = 7a + 26

7a + 14 = 7a + 26

14 = 26

No solutions

500

Solve the following equation for x:
4(2x - 3) - 5(x + 1) = 3x - 17

4(2x - 3) - 5(x + 1) = 3x - 17

8x - 12 - 5x - 5 = 3x - 17

3x - 17 = 3x - 17

-17 = -17

Infinitely many solutions

Linear Inequalities

100

Solve the following inequality and graph the solution on a number line:
x + 3 > 7

x > 4

open dot

arrow -->

200

Solve the following inequality:
2x - 5 ≤ 11

2x - 5 ≤ 11

2x ≤ 16

x ≤ 8

closed dot

arrow <--

300

Solve the following inequality
-3x + 4 < -11

-3x + 4 < -11

-3x < -15

x > 5

open dot

arrow -->

400

Solve the inequality:
-3x + 1 < 10

-3x + 1 < 10

-3x < 9

x > -3

open dot 

arrow -->

500

Solve the following inequality. Graph the solution on a number line:
4(x - 2) + 3 > 2(x + 1) - 5

4(x - 2) + 3 > 2(x + 1) - 5
4x - 8 + 3 > 2x + 2 - 5

4x - 5 > 2x - 3

2x - 5 > -3

2x > 2

x > 1

open dot 

arrow --> 

Proportions

100

Solve for x:

3/x = 12/20

3/x = 12/20

3*20 = 12x

60 = 12x

x = 5

200

Solve for y:

(y+2)/5 = y/3

(y+2)/5 = y/3 

3(y+2) = 5y

3y + 6 = 5y

6 = 2y

y = 3

300

Solve for x:

7/(2x - 1) = -4/(x+3)

7/(2x - 1) = -4/(x+3)

7(x+3) = -4(2x - 1)

7x + 21 = -8x + 4

15x + 21 = 4

15x = 25

x = 25/15 = 5/3

400

Solve for a:

(3a+2) / (a - 1) = 5/2

(3a+2) / (a - 1) = 5/2

2(3a + 2) = 5(a - 1)

6a + 4 = 5a - 5

a + 4 = -5

a = -9

500

Solve for x:

(-2x - 5) / (3 - x) = -7 / -4

(-2x - 5) / (3 - x) = -7 / -4

-4(-2x - 5) = -7(3 - x)

8x + 20 = -21 + 7x

x + 20 = -21

x = -41

Literal Equations

100

Solve for a:

h = a + 7

a = h - 7

200

Solve for b: 

j = bH

b = j/H

300

Solve for B:

B/Q = d + f³

B= Q(d + f³)

400

Solve for b: 

Gb = m / R

Gb = m / R

b = m / (RG)

500

Solve for A:

G = 5BA - Q

G = 5BA - Q

G + Q = 5BA 

A = (G + Q) / (5B)

Consecutive Integers

100

The sum of three consecutive integers is 51. Find the value of the greatest of the three.

18

200

Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 63, find Christopher's age.

Christopher is 23 years old 

300

The sum of three consecutive odd integers is 75. Find the value of the middle of the three.

25

400

The lengths of the four sides of a quadrilateral (in meters) are consecutive even integers. If the perimeter is 52 meters, find the value of the longest of the four side lengths.

16 meters

500

The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 86 inches. Find the length and width of the rectangle.

21 & 22 inches