Verified answer

For the first problem:

Subtract 3x from both sides.

1/3 = -1/2

For which values of x does 1/3 = -1/2?

None, 1/3 and -1/2 are both constant, and they are not equal.

No solutuion.

For the second problem:

Expand both sides:

(-3)(4b) + (-3)(-10) = (1/2)(-24b) + (1/2)(60)

-12b + 30 = -12b + 30

For which values of b does -12b + 30 = -12b + 30?

Subtract 30 from both sides.

-12b = -12b

Divide both sides by -12.

b = b

When does b = b?

For all values of b.

For the third problem:

Expand the left side.

(1/2)(2x) + (1/2)(-5) = 4x - 1

x - 5/2 = 4x - 1

Subtract x from both sides.

-5/2 = 3x - 1

Add 1 to both sides.

-3/2 = 3x

Divide both sides by 3.

-1/2 = x

So x = -1/2

First one can't happen, if you subtract 3x from both sides you get 1/3 = 1/2 and we know that's not right. Do you have a typo?

-3(4b-10) = 1/2(-24b+60) (multiply by the number on the outside of the parentheses)

-12b + 30 = -12b+30

the 2 sides of the equation are the same so b would equal anything and everything

1/2(2x-5) = 4x-1

2x - 5 = 8x - 2 (multiply both sides by 2)

2x - 2x - 5 = 8x - 2x - 2 (subtract 2x from each side)

-5 = 6x - 2

-5 + 2 = 6x - 2 + 2 (add 2 to both sides)

-3 = 6x

x = -3/6 or -1/2

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

1/3 = - 1/2 (not logical, no solution!)

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-3 (4b-10) = 1/2 (-24b+60)

-12b + 30 = -12b + 30

30 = 30

every number you put into it will fit. The answer is R (real numbers).

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1/2 (2x-5) = 4x-1

x - 5/2 = 4x - 1

1 - 5/2 = 3x

-3/2 = 3x

x = -1/2

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

To solve get all the x's on one side:

In this case the x's will cancel leaving the statement not solvable

-3(4b-10) = 1/2 (-24b+60)

I would distribute first to get rid of parenthesis

-12b + 30 = -12b +30

again they cancel leaving 30=30 so the answer would be: true all real numbers.

1/2(2x-5)=4x-1

Distribute

x- 5/2= 4x-1

x's to one side

-3/2=3x

x= -1/2

Move the variables to one side

Move the constants to the other side

Divide by the coefficient attached to the variable

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

-3x -3x

+1/2 +1/2

(2/6 + 3/6)

5/6

hmmm... good question. I don't know. Pretty sure there isn't an answer.