I need some help, it would be greatly appreciated?

Question

I am having a few problems, I know the answers from plugging them in, just dont know how to find them by working them out. could you demonstrate the proper ways to work them?

1a,
2(1+x)=3x
X=2

1b,
(x+1)(x-1)=x^2-x
x=1

1c,
(x+1)^2=x^2
x=-1/2

your help will be appreciated

Answer 1

Question 1a
2 + 2x = 3x
2 = x

Question 1b
x ² - 1 = x ² - x
x - 1 = 0
x = 1

Question 1c
(x + 1) ² = x ²
x ² + 2x + 1 = x ²
2x = - 1
x = - 1 / 2

Answer 2

1a,
2(1+x)=3x so first of all multiply 2 in the (1 + x ) you should multiply the 2 in all of the Parenthesis items so ( 2*1 + 2 *x ) = 2+ 2x so you have summerized one part the other part is 3x it is perfect the next step is that put the items with x in one part of the "= " and others in other part of " = " be carefull change the place of each item make posetive item negative and vise versa so 2 = 3x - 2x and x = 2
1b (x + 1 )(x - 1) = x * x + x * (-1) + 1 * x + 1 * (-1) = x^2 - x + x -1 = x ^2 -1
x^2 - 1 is one part the other part is x ^ 2 - x
i said that put the items with x in one side of "="
x^2 - x ^2 + x = 1 so x = 1
1c (x + 1 )^2 = (x+1)(x + 1) = x *x + x*1 + 1 * x + 1 * 1 = x^2 +x + x +1 = x^2 + 2x + 1 it is one side other side is x ^ 2
x^2 + 2x + 1 = x ^ 2 so x ^2 - x^2 + 2x = -1 so 2x = -1 so x= -1/2
i will be so happy if i can help you

Answer 3

1 a)
2(1 + x) = 3x
first expand left hand side 2(1 + x) = 2 + 2x
2 + 2x = 3x
subtract 2x from both sides
2 + 2x - 2x = 3x - 2x
2 = x

1b)
(x + 1)(x - 1) = x^2 - x
but (x + 1)(x - 1) = x^2 - 1 (since (a + b)(a - b) = a^2 - b^2)
x^2 - 1 = x^2 - x
subtract x^2 from both sides
-1 = -x
x = 1

1c
(x + 1)^2 = x^2
x^2 + 2x + 1 = x^2
subtract x^2 from both sides
2x + 1 = 0
2x = -1
x = -1/2

Answer 4

1a
2(1+x) = 3x
Multiply the factor 2 into the terms in the brackets.
2 + 2x = 3x
Subtract '2x' from both sides
2 + 2x - 2x = 3x - 2x
2 = x

1b
(x+1)(x-1) = x^2 - x
Using F O I L multiply out brackets
x^2 - x + x - 1 = x^2 - x
x^2 - 1 = x^2 - x
-1 = -x
x = 1

1c
(x+1)^2 = x^2
Using F O I L again
x^2 + 2x + 1 = x^2
2x + 1 = 0
2x= -1
x = -1/2

Answer 5

1a)
Distribute the 2 by multiplying:
2 + 2x = 3x

Subtract 2x from both sides:
2 + 2x - 2x = 3x - 2x

2 = x

1b.
(x + 1)(x - 1) = x^2 - x

Use FOIL to multiply (x+1)(x-1): first, outer, inner, last
x^2 + x - x - 1 = x^2 - x

Add one to each side. Subtract x^2 from each side. Add x to each side.
-1 + x + 1 = x^2 - x^2 - x + 1 + x
x = 1

(x + 1)(x + 1) = x^2
FOIL again
x^2 + x + x + 1 = x^2

Subtract x^2 from each side. Subtract -1 from each side
x^2 - x^2 + 2x = -1
2x = -1
x = -1/2

Answer 6

First expand the left side by multiplying it out. Then get your x terms on one side.

For example,

1a)

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

Good Luck!

Answer 7

You just need to follow the order of operations

1a)
2(1+x)=3x use the distributive property
2+2x=3x subtract 2x from both sides
2=x

Answer 8

1a
take 2(1+x) and make it 2+2x
take the 2 and put it on the other side 2x=3x-2
put 3x on the other side -x=-2
since both are negitive x=2
1b
take (x+1)(x-1) and make it x^2+x-x-1 which is x^2-1
cancel out x^2 and you get -1=-x which is x=1
1c
I couldn't get this right but at least I tried.

Answer 9

1a. 2(1+x)=3x ---------------distribute the 2
----- 2 + 2x = 3x--------------collect like terms by subtracting 2x from both sides
2 = x which is the same as x = 2

1b. (x+1)(x-1)=x^2-x--------multiply the left side out
x^2-1= x^2-x-------------collect like terms by subtracting x^2 from both sides
-1 = -x ------------------divide by -1
1=x

1c. (x+1)^2=x^2-------------multiply out the left side
x^2 + 2x + 1 = x^2 ---------collect like terms by subtracting x^2 from both sides
2x + 1 = 0
2x =-1
x = -1/2

Hope this helps.

Answer 10

a) 2+2x=3x
2+2x-2x=3x-2x
2=x

b) x²-1 = x²-x
x²-x²-1=x²-x²-x
-1=-x
1=x

c) x²+2x+1 = x²
x²-x²+2x+1=x²-x²
2x+1=0
2x+1-1=0-1
2x=-1
2x/2=-1/2
x=-1/2