Yep!Observe that if [MATH]a - b = c[/MATH], then [MATH]a - c = b[/MATH]. We can adjust the equation as follows:
[MATH]\frac{z - 2.1}{2.2 - 2.1} = 0.03573 - 0.035[/MATH]
When a variable is buried within an expression like this, you "dig it out" piece by piece by moving everything else to the other side of the equals sign. Do keep in mind that both sides must remain equal at all times, so if you perform an operation to one side, you must perform the same operation to the other side.
We begin with this:
[MATH]0.035 = 0.03573 - \frac{z - 2.1}{2.2 - 2.1}[/MATH]
Observe that if [MATH]a - b = c[/MATH], then [MATH]a - c = b[/MATH]. We can adjust the equation as follows:
[MATH]\frac{z - 2.1}{2.2 - 2.1} = 0.03573 - 0.035[/MATH]
This has moved one of the terms away from [MATH]z[/MATH], to the other side of the equals sign.
Next, we will need to get [MATH]z[/MATH] out of the fraction. What happens if we multiply both sides of the equation by [MATH](2.2 - 2.1)[/MATH]?
I'm thinking the factor (0.03573 - 0.02781) is part of the equation.
I would have simplified the subtractions that can be evaluated, first.
0.035=0.03573−0.1z−2.1(0.007920)
No problem, it just becomes this instead:Note: I think my picture (equation) was a bit unclear. The numbers in the bracket to the right are indeed part of the whole equation. Sorry for that!
Specifically, we multiply it on the right. I think by "add" you meant something like "put", but it's an important distinction!Thank you for your reply. If we multiply on both sides, it cancels out on the left and we add it to the right part of the equation.
No problem, it just becomes this instead:
[MATH]0.035 = 0.03573 - \frac{z - 2.1}{2.2 - 2.1}(0.03573 - 0.02781)[/MATH]
And the same first step is performed:
[MATH]\frac{z - 2.1}{2.2 - 2.1}(0.03573 - 0.02781) = 0.03573 - 0.035[/MATH]
Specifically, we multiply it on the right. I think by "add" you meant something like "put", but it's an important distinction!
Since there's an extra multiplication this time (after the correction), the next step is to divide both sides by [MATH](0.03573 - 0.02781)[/MATH]. Here's what that looks like:
[MATH]\frac{z - 2.1}{2.2 - 2.1} = \frac{0.03573 - 0.035}{0.03573 - 0.02781}[/MATH]
Then we multiply by [MATH](2.2 - 2.1)[/MATH]:
[MATH]z - 2.1 = \frac{0.03573 - 0.035}{0.03573 - 0.02781}(2.2 - 2.1)[/MATH]
Nearly there now! Only one step remains.
Since the numbers are a bit scattered, this is the basic form of the alegbra:
[MATH]a = b - c\frac{z - d}{e}[/MATH]
[MATH]c\frac{z - d}{e} = b - a[/MATH]
[MATH]\frac{z - d}{e} = \frac{b - a}{c}[/MATH]
[MATH]z - d = e\frac{b - a}{c}[/MATH]
[MATH]z = e\frac{b - a}{c} + d[/MATH]
Great
Great, thank you for the detailed walkthrough. That sure helps me a lot. Now, I assume we just add +2.1 on both sides, to have z alone. After that, can I just put it into the calculator?
Hi Nikita. You mean the most complicated to deal with, yes? Otherwise, it's just an expression for the number 0.00792.… [the factor (0.03573 - 0.02781) appearing on the right-hand side] is also the part that I found to be the most complicated.
The phrase "get it on the other side" is not technically correct because it usually refers to adding (or subtracting) a term. Perhaps, you were thinking that division is the way to "eliminate" the factor 0.00792, on the right-hand side. If that's what you were thinking, then, yes, division could be one way to proceed. Just remember that when you divide a sum or difference by something, you must divide each term. We haveDo I divide by 0.007920 to get it on the other side? …