Simple Equation to everybody but not me
- Thread starter Albertino
- Start date
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,541
First, let's make it a little clearer; it's dangerous to use "x" to mean both multiplication and a variable, as you presumably do. Here is what I think it is:
An operation is defined as [imath]a * b = 3a - 5b[/imath]. Find the value of [imath]x[/imath] in [imath]7 * (x * 4) = 1[/imath].
What this means is that "*" is the symbol for a made-up operation (not multiplication) that is performed by subtracting 3 times the first operand, minus 5 times the second operand. For example, [imath]2 * 3 = 3(2) - 5(3)=6-15=-9[/imath].
Now you are to find the value(s) of [imath]x[/imath] such that [imath]7 * (x * 4) = 1[/imath].
I can imagine several ways to try to solve [imath]7 * (x * 4) = 1[/imath]; one would be to first solve [imath]7 * y = 1[/imath] for [imath]y[/imath], and then use the result and solve [imath]x * 4 = y[/imath] for [imath]x[/imath]. Another would be to rewrite [imath]7 * (x * 4) = 1[/imath] using the definition twice, and then solve the remaining ordinary equation.
I'm hoping that what I've explained will give you a start, so you can show us what you understand of the problem, and/or what you try in order to take it from where I've left it.
It will also be helpful if you tell us your context: Are you taking a course in which this was taught (what course?), or did you come across the problem outside of what you are learning? The more we know about you, the better we can help you figure it out.
Posting Guidelines (Summary)
Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com
By the way, is it a typo(Sorry, maybe I'm wrong) in "What this means is that "*" is the symbol for a made-up operation (not multiplication) that is performed by subtracting 3 times the first operand, minus 5 times the second operand." If not, why subtracting 3 times the first operand, minus 5 times the second operand? Thanks again.
Following the advice given above:
Substitute :
Y = x * 4 = 3x - 20 ......... (according definition of '*' provided in the problem statement)
7 * Y = 7 * 3x - 7 * 20 ........( assuming distributive property of '*')
7*Y = ? ...... (finish it and show your work)
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,541
I wrote it a little awkwardly (because subtraction can be awkward); but surely you see that 3a-5b means "3 times a minus 5 times b", and that we are subtracting?
That is, stated a little more normally, we are subtracting 5 times the second from 3 times the first. I wanted to keep the same order, which made it more awkward. (My first attempt was worse: "subtracting from 3 times the first operand, 5 times the second operand.")
Which means the awkward form that I corrected is their fault, not yours. That's fine; it had to be cleared up either way, and I didn't assign blame.
I am a little surprised that they would do that, even if what they used was [imath]\times[/imath] rather than x; but what can I say? (I won't demand to see a picture of the original.)
Have you worked out the problem yet?
Harry_the_cat
Elite Member
- Joined
- Mar 16, 2016
- Messages
- 3,740
Correct!
Check your solution by showing that 7*(3x8-20) ie 7*4 equals 1.