Question

Help with the following:

a. 3x+7=-x-1

b. 1-2x+5=4x-3

c. 4x-2+x=-2+2x

d. 3x-4+1=2x-5+5x

solve for x

(please show work)

Answer 1

Answers:

a. 3x+7=-x-1

Move -x to the other side. Sign changes from -x to +x.

3x+x+7= -x+x-1

3x+x+7= -1

4x+7= -1

4x+7-7= -1-7

4x= -8

divide by 4 for both sides

4x/4= -8/4

x= -2

b. 1-2x+5=4x-3

1+5-2x= 4x-3 - combine like terms

6-2x= 4x-3

move 6 to the other side

6-6-2x= 4x-3-6

-2x= 4x-9

Move 4x to the other side

Sign changes from 4x to -4x

-2x-4x= 4x-4x-9

-6x= -9

divide by -6

-6x/-6= -9/-6

9/6- reduce. divide by 3. 9/3= 3 , 6/3= 2

x= 3/2 and x= 1 1/2

c. 4x-2+x=-2+2x

4x+x-2= -2+2x

5x-2= -2+2x

5x-2x-2= -2+2x-2x

3x-2= -2

3x-2+2= -2+2

3x=0

divide by 3

3x/3= 0/3

x= 0

d. 3x-4+1=2x-5+5x

3x-3= 2x+5x-5

3x-3= 7x-5

3x-7x-3= 7x-7x-5

3x-7x-3= -5

-4x-3= -5

Move -3 to the other side

-4x-3+3= -5+3

-4x= -2

divide by -4

-4x/-4= -2/-4

x= 2/4 or reduce x= 1/2 ( divide by -2 : -2/-2= 1 , -4/-2= 2

Answer: x= 2/4 and x= 1/2

Answer 2

Answer and step-by-step explanation:

a. 3x+7=-x-1

Bring x into 1 side and the other number into another side, we got:

3x + x = -1 - 7

4x = -8

Divide both side by 4:

4x / 4 = -8/4

x = -2

b. 1-2x+5=4x-3

1 + 5 + 3 = 4x + 2x

9 = 6x

Divide both side by 6:

x = 9/6 = 3/2 or 1.5

c. 4x-2+x=-2+2x

4x + x - 2x = -2 + 2

3x = 0

x = 0

d. 3x-4+1=2x-5+5x

3x - 2x - 5x = -5 + 4 - 1

-10x = -2

x = -2/-10

x = 2/10 = 1/5 or 0.2

Hope this helped :3