# 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:

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

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

Simplify the Following:

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

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

**Answers:**

Type One:

- 2
- 4
- 0
- -7
- 7
- -14
- 6
- 7
- 5
- 1

Type Two:

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

Type Three:

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