Basic Algebra Problems

Last week I wrote some fifth grade math problems. Today, I am going to put up a few simple algebra problems (of different types) with the answers at the end of the post.

Questions:

First Type: Solving Equations

Solve for x:

1. 4x = 8
2. 2x + 7 = 15
3. x + 6 = 6
4. 5 – (x + 2) = 10
5. 4x = 7 + 3x
6. 2x = 14 + 3x
7. 3x = 6 + 2x
8. 7x = 49
9. 2(x + 5)= 20
10. 10(2x + 7) = 90

Second Type: Addition and Subtraction (remember only like terms can be added and subtracted).

Simplify the Following:

1. 2x + 3y + 3x + 9y
2. 2x + 7xy + 12x
3. 3a + 3ab + 3ac + 3ad
4. 2a + 2b – 8b + 7ab + 5b
5. 3a + 4a + 5b
6. 3abcd + 3abc – 5abcd
7. 5 + 7a + 2 + 3a
8. a – a
9. x + 4 – 5x + 1
10. y + 2 + y

Third Type: Linear Equations

What is the slope and y-intercept of the following lines. Note, you do not have to draw them. Just get them in the form y = mx + c, where m = slope and c= y-intercept

1. y = 2x + 4
2. y = 5x -2
3. 2y = 8x -4
4. 3y = 6x – 7
5. 10y = 170x + 650
6. x + 6 = y
7. y + 3 = x
8. 2y + 6x = 1
9. y = 5 – x
10. x – y = 3

Answers:

Type One:

1. 2
2. 4
3. 0
4. -7
5. 7
6. -14
7. 6
8. 7
9. 5
10. 1

Type Two:

1. 5x + 12y
2. 14x + 7xy- could be written as 7x(2 + y)
3. 3a + 3ab + 3ac + 3ad- cannot be simplified as there are no like terms unless you factorize it to 3a(1 + b + c + d)
4. 7a + 7ab – b
5. 7a + 5b
6. 3abc – 2abcd- could be factorized to abc(3 – 2d)
7. 7 + 10a
8. 0
9. 5 – 4x
10. 2y + 2- factorize to 2(y + 1)

Type Three:

1. slope = 2, y-intercept = 4
2. slope = 5, y-intercept = -2
3. slope = 4, y- intercept = -2
4. slope = 2, y-intercept = 7/3
5. slope = 17, y-intercept = 65
6. slope = 1, y-intercept = 6
7. slope = 1, y-intercept = -3
8. slope = -6, y-intercept = 1/2 (or 0.5)
9. slope = -1, y-intercept = 5
10. slope = 1, y-intercept = -3

Please leave a comment and tell me how you went or suggest some more algebra problems I could add!

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