multiply the equation by a power of 10 to write an equivalent equation with integer coefficients:
#1. 4.15x+3.01=10.9x+1.29
#2. 1.596y-3.08=0.9y
this is the 2nd time I'm posting this question. but the last reply I got was confusing. can you please show me how to do at least one of these? thnxx
#1. Multiply both sides by 100 (to convert the 1.29 and 4.15 to integers)
#2. Multiply both sides by 1000.
Do you understand why?
like in number 1, do I have to multiply 3.01 and 1.29 by 100 too?
and also, when I multiply both sides, do I keep the x (or y)?
Can you please check if I did these right?
1. 415x+301=1009x+129
2. 1596y-3080=900y
I know I'm being annoying and stupid, but I'll stop posting. thanxxx!
Yes, every term gets multipled by the same factor. You keep the x and the y as is. Only the coefficients get multiplied
so the answers that I posted.. are those correct?
Of course! Let's start with the first equation: 4.15x + 3.01 = 10.9x + 1.29.
To write an equivalent equation with integer coefficients, we need to get rid of the decimal numbers. To do this, we can multiply the equation by an appropriate power of 10 that eliminates the decimals.
Step 1: Identify the number of decimal places in the equation. In this case, we have two decimal places, as seen in the numbers 4.15, 3.01, 10.9, and 1.29.
Step 2: Multiply both sides of the equation by a power of 10 equal to 10 raised to the number of decimal places. Since we have two decimal places, we will multiply by 10^2 = 100.
Here's the equation after multiplying by 100:
100 * (4.15x + 3.01) = 100 * (10.9x + 1.29)
Simplifying this equation gives us:
415x + 301 = 1090x + 129
Now we have an equivalent equation with integer coefficients: 415x + 301 = 1090x + 129. You can then proceed to solve this equation as you would with any other equation.
Now, to address the second equation you've provided: 1.596y - 3.08 = 0.9y.
We'll follow the same steps as before. In this equation, we have three decimal places: 1.596, 3.08, and 0.9.
Multiply both sides of the equation by 10 raised to the power of 3, which is 1000:
1000 * (1.596y - 3.08) = 1000 * (0.9y)
Simplifying this equation gives us:
1596y - 3080 = 900y
The resulting equation is 1596y - 3080 = 900y, which now has integer coefficients.
I hope this explanation clarifies the process for you. Please let me know if you have any further questions!