-4(x+0.5) = -2(2x-1)
-4(x+0.5) = -2(2x+1)
-4(x+0.5) = -2(1-2x)
-4(x=0.5) = -2(4-2x)
To solve these equations, we can start by distributing the numbers outside the parentheses to the terms inside the parentheses. Let's take a look at each equation step by step:
1) -4(x + 0.5) = -2(2x - 1):
Distribute -4 to x and 0.5:
-4x - 2 = -4x + 2
2) -4(x + 0.5) = -2(2x + 1):
Distribute -4 to x and 0.5:
-4x - 2 = -4x - 2
3) -4(x + 0.5) = -2(1 - 2x):
Distribute -4 to x and 0.5:
-4x - 2 = -2 + 4x
4) -4(x = 0.5) = -2(4 - 2x):
There seems to be an error in this equation. It should be expressed as:
-4(x - 0.5) = -2(4 - 2x)
Distribute -4 to x and -0.5:
-4x + 2 = -8 + 4x
Now, let's solve each equation:
1) -4x - 2 = -4x + 2:
We can combine like terms:
-4x + 4x = 2 + 2
The x terms cancel out, leaving us with:
0 = 4
This equation is inconsistent, meaning there is no solution.
2) -4x - 2 = -4x - 2:
We can combine like terms:
-4x + 4x = -2 + 2
Again, the x terms cancel out:
0 = 0
This equation is dependent, meaning any value of x will satisfy it. It has infinite solutions.
3) -4x - 2 = -2 + 4x:
Let's rearrange the equation to group the x terms on one side:
-4x - 4x = -2 + 2
Combine like terms:
-8x = 0
Divide both sides by -8 to solve for x:
x = 0
The solution to this equation is x = 0.
4) -4x + 2 = -8 + 4x:
Again, let's rearrange the equation to group the x terms:
-4x - 4x = -8 - 2
Combine like terms:
-8x = -10
Divide both sides by -8 to solve for x:
x = 1.25
The solution to this equation is x = 1.25.