Algebra Help?

Question

1.) -2(x + 5) - 7 = 3x + 2(x - 5)

2.) 3(4x + 2) - 6x = 5x - 5(2+ x)

3.) 5(6x - 1) - 10x + 5 = 4(x + 10) - 4x

4.) -6(4 - x) + 12 = 3x - (x - 4)

Distributing and Combining, how?

Answer 1

Okay, here we go:

1) -2x-10-7 = 3x+2x-10
-2x-17 = 5x - 10
-2x -5x = -10+17
-7x = 7
x = -1

2) 12x+6-6x = 5x-10-5x
6x+6 = -10
6x = -10 - 6
6x = -16
x = -8/3

3) 30x-5-10x+5 = 4x+40-4x
20x = 40
x =2

4) -24+6x+12 = 3x-x+4
6x-12 = 2x+4
6x-2x = 4+12
4x=16
x = 4

See? It's quite easy.

Answer 2

distributing is when you multiply through the parenthesis.
ex. 5(a + b) = 5a + 5b
combining is when you combine like terms
ex. 2x + 3x - 5 you can combine 2x and 3x b/c they both have an x. so you get 5x - 5

1.) -2(x + 5) - 7 = 3x + 2(x - 5)
first distribute the -2 on the left
-2x -10 - 7 = 3x + 2(x-5)
now the 2 on the right
-2x - 10 - 7 = 3x + 2x -10
now combine all the stuff w/ x together on each side, and the numbers w/o x
-2x - 17 = 5x - 10
add 2x to both sides
-2x + 2x - 17 = 5x + 2x - 10
-17 = 7x - 10
add 10 to both sides
-17 + 10 = 7x - 10 + 10
-7 = 7x
divide both sides by 7
-1 = x

Now you should be able to do the rest no problem!

Answer 3

1. -2x + -10 -7 = 3x + 2x -10
-2x + - 17 = 5x -10
-2x = 5x + 7
3x = 7
x = 7/3

2. 12x + 6 -6x = 5x - 10 - 5x
6x + 6 = -10
6x = -4
x = -4/6
x = -2/3

3. 30x - 5 - 10x + 5 = 4x + 40 - 4x
20x = 40
x = 20 / 40
x = 1/2

4. -24 + 6x + 12 = 3x -x + 4
6x - 12 = 3x + 4
6x = 3x + 16
3x = 16
x = 16/3

Answer 4

1. -2x + -10 -7 = 3x + 2x -10
-2x + - 17 = 5x -10
-2x = 5x + 7
3x = 7
x = 7/3

2. 12x + 6 -6x = 5x - 10 - 5x
6x + 6 = -10
6x = -4
x = -4/6
x = -2/3

3. 30x - 5 - 10x + 5 = 4x + 40 - 4x
20x = 40
x = 20 / 40
x = 1/2

4. -24 + 6x + 12 = 3x -x + 4
6x - 12 = 3x + 4
6x = 3x + 16
3x = 16
x = 16/3

Answer 5

Lets take the first equation

-2(x+5)-7 = 3x+ 2(x-5)
i.e. -2x-10-7 = 3x +2x -10
i.e. 3x+2x+2x = 7
which makes the value of x =1

The second one:
12x + 6 - 6x = 5x -10 -5x
i.e. 6x + 6 = -10
i.e. 6x = -16
which makes the value of x = -8/3

The third one:
30x -5 -10x + 5 = 4x + 40 - 4x
i.e. 20x = 40
which makes the value of x = 2

The final one:
-24 + 6x + 12 = 3x - x + 4
i.e. -18x +12 = 2x +4
i.e. 12 - 4 = 2x + 18x
i.e. 8 = 20x
which makes the value of x = 2/5

Hope this helps you dear!

Answer 6

When you distribute and combine, simply move along at a steady pace:

First, distribution: Multiply everything in the parentheses by the item which is outside of the parentheses:

1) -2x - 10 - 7 = 3x + 2x - 10

Next, combine like terms. This means add (or subtract, as the case may be) all things that have x's to each other, and also add (or subtract) all things that don't to each other:

1) -2x - 17 = 5x - 10

Next, add the same thing to both sides of the equation, and it maintains its equality. In this case, add (2x + 10)

1) -2x - 17 + 2x + 10 = 5x - 10 + 2x + 10

Now, recombine like terms:

-7 = 7x

Divide both sides by 7, and you get:

x = -1

Now, repeat these steps for the other problems, and you're done. :-)