Okay, i need help. I'm solving linear equations in intermediate algebra. My problem is that I never know which number to subtract first.
Ex:
5y-8=-18
To get the right answer (-2), they move they add the 8 to both sides.
But on 27w-64=-37
They move the 37 to get the correct answer (1)
Help. All of my problems are set up the same, but each one needs a different side. How do I know which one to move?
27w-64=-37
I would add 64 to both sides
I want everything that is times w on one side
and
everything that is just a number on the other side
27 w - 64 + 64 = -37 + 64
27 w = 27 divide bot sides by 27 now
27 w/27 = 27/27
w = 1
That's not how they did it though.
I keep choosing the wrong side. I don't understand.
I can not imagine what they did and why.
But just remember you want to get your unknown variable (x or whatever) alone on one side (it does not matter which side really)
and you want to get everything else on the other side.
Like I could do this problem backwards
27w-64=-37
add 37 to both sides
27 w - 64+37 = -37 +37
27 w - 27 = 0
now add 27 to both sides
27 w = 27
w = 1
That is perfectly ok, but takes longer because it requires another step to get w alone on one side.
What about the other equation though? Because I'm doing some where if I pick the wrong side, the answer comes out with the wrong sign.
That should not happen if you do it correctly even if differently.
If you add the same thing to both sides, it does not change the answer.
If you subtract the same thing from both sides, it does not change the answer.
If you multiply every term on both sides by anything but zero, it does not change the answer.
If you divide everything on both sides by anything but zero, it does not change the answer.
If the answer changes, you made an arithmetic mistake.
Remember
-*- = +
-*+ = -
+*+ = +
Ugh. :(
Here's an example of what i'm doing:
MINE:
3y-18=-6y
3y+6y-18=-6y+6y
9y-18
9y/9 = -18/9
y=-2
Theirs:
3y-18=-6y
-3y+3y-18=-6y-3y
-9y/9y = -18/9
y=2
They're saying 2 is right. I'm so confused.
MINE:
3y-18=-6y
3y+6y-18=-6y+6y
9y-18 continue with right 9 y - 18 = 0
9y/9 = -18/9 then add 18 both sides 9 y=18
y=-2 then y = 2
I really don't know how to solve this x+6y=24 3x-12y=-18
When solving linear equations, it's important to understand the goal: to isolate the variable on one side of the equation. This means that the variable should be alone on one side, usually with a coefficient of 1. To achieve this, we perform algebraic operations to simplify the equation and get the variable by itself.
To determine which side to move the numbers to, you want to think about the goal of isolating the variable. To do this, it's helpful to follow a systematic approach:
1. Start by simplifying both sides of the equation as much as possible. Combine like terms, distribute any coefficients, and simplify.
2. Look for any terms containing the variable. These are the terms we want to isolate.
3. Determine whether the terms containing the variable have positive or negative coefficients.
4. Move all terms not containing the variable to the other side of the equation by performing the opposite operation.
Here's an example using the equation 5y - 8 = -18:
1. Simplify both sides by combining like terms:
5y - 8 = -18
2. Identify the terms containing the variable:
5y
3. Notice that the coefficient of 5y is positive (5).
4. Since we want to isolate the variable, we move all terms not containing the variable (in this case, -8) to the other side of the equation:
5y = -18 + 8
Simplifying:
5y = -10
Now, let's consider the equation 27w - 64 = -37:
1. Simplify both sides:
27w - 64 = -37
2. Identify the terms containing the variable:
27w
3. Observe the coefficient of 27w (27).
4. To isolate the variable, we need to move all terms not containing the variable (in this case, -64) to the other side of the equation:
27w = -37 + 64
Simplifying:
27w = 27
In summary, when deciding which side to move the numbers to, focus on isolating the variable. If the terms containing the variable have a positive coefficient, move the terms without the variable to the opposite side of the equation. Conversely, if the terms containing the variable have a negative coefficient, move the terms without the variable to the same side as the variable. Following this approach systematically will help you determine which side to move the numbers to in order to solve linear equations.