Thread: Trying to strengthen my math skills

I am trying to advance in my math skills and took some time to do a little algebra. I worked these problems and want to know if I got them right.

23 = p - 4
p - 4 -23
p - 27

-3x + 5 = 2
-3x = 2 - 5
-3x/-3x = -3/-3
x = 1

4 + d = 4 - 5 (d - 1) - 3
4 + d = 4 - 5d + 5 - 3
4 + d = -5d + 6
4 - 6 = -5d - d
-2 = -6d
-2/-6 = 1/3d

9/7 + 8/6x = -1/6x + 1
42 (3/4 + 2/6x = -1/6x + 1)
18 + 14x = -7x + 42
18-42 = -7x+ 42
-24 = -12x
-24 * 3/-21 * 3
x = 8/7

x + 2/8 + x-2/12 = 3
24 (x + 2/8 + x - 2/12 = 3) = 3 8 24/72
3x + 6 + 2x - 4 = 72
3x + 2x = 72 - 6 + 4
5x/5 70/5 = 14
x = 14

the perimeter of a triangle is 144. What are the consecutive even integers for each side?
x + x + 2 + x + 4 = 144
3x + 6 = 144
144 - 6 = 138
3x/3 138/3 = 46
46...48...50 are the consecutive even integers

5z - 12 >= 6z - 8 >= 4
5z - 6z >= 12 - 8 >= 4
-1z >= 4 >= 4
cannot be solved

5 (4 - 3x) < 7 (3 - 4x) + 12
20 - 15x < 21 - 28x + 12
20 - 12 - 12 < 28x - 15x
-13 < -13x
< 1

8x - 23/6 + 1/3 >= 5/2x
I couldn't figure this one out but I tried it.
2 * 8x - 23 + 4 >= 6 * 5
16x - 23 >= 4 >= 30

I think I got all of those right.

23 = p - 4
p - 4 -23
p - 27

No, you got your equals and minus signs in a mess.

-3x + 5 = 2
-3x = 2 - 5
-3x/-3x = -3/-3
x = 1

No, in the 3rd line you've got one x too many.

4 + d = 4 - 5 (d - 1) - 3
4 + d = 4 - 5d + 5 - 3
4 + d = -5d + 6
4 - 6 = -5d - d
-2 = -6d
-2/-6 = 1/3d

Your last line you went wrong - I think you meant:

-2/-6 = -6d/-6
1/3 = d

In general, you know what you're doing - you need to be a *little* more careful when writing stuff down because the teacher will come down on little things like this.


The others also all seem to need attention - I'm trying to figure out your thinking when you did:

9/7 + 8/6x = -1/6x + 1
42 (3/4 + 2/6x = -1/6x + 1)

... because it doesn't look right to me. Unless there's something I'm missing.


Good job, though - exercises really do help.