(5y-3)/3 - (2y-1)/2=1
note: the divide signs are the fraction bars.
-5(-2(x-1) - (x+1))=9
.08n-.09(n-2)=5-.08
-2(3-(x-1)+3x) + 2(x-3-5(x-3)-x)=10
please show me how you got the answers thanks
#1.
(5y-3)/3 - (2y-1)/2=1
[(5y-3)/3 - (2y-1)/2 = 1]*6
2(5y-3) - 3(2y-1) = 6
10y - 6 - 6y + 3 = 6
4y - 3 = 6
4y = 9
y = 9/4
#2.
-5(-2(x-1) - (x+1)) = 9
-5(-2x + 2 - x - 1) = 9
-5(-3x + 1) = 9
15x - 5 = 9
15x = 14
x = 14/15
#3.
.08n-.09(n-2)=5-.08
0.08n - 0.09n + 0.18 = 4.92
-0.01n = 4.74
n = -474
#4.
-2(3-(x-1)+3x) + 2(x-3-5(x-3)-x)=10
-2(3-x+1+3x) + 2(x-3-5x+15-x)=10
-2(2x + 4) + 2(12 - 5x) = 10
-4x - 8 + 24 - 10x = 10
-14x + 16 = 10
-14x = -6
x = 6/14 = 3/7
hope this helps~ :)
Thanks! :)
Sure, I'll be happy to help you solve these equations. Let's go through each equation step by step.
1. (5y - 3)/3 - (2y - 1)/2 = 1
To begin, we need to remove the fractions by finding a common denominator. The least common multiple of 3 and 2 is 6, so let's multiply both sides of the equation by 6 to clear the fractions:
6 * [(5y - 3)/3] - 6 * [(2y - 1)/2] = 1 * 6
This simplifies to:
2(5y - 3) - 3(2y - 1) = 6
Distribute the coefficients:
10y - 6 - 6y + 3 = 6
Combine like terms:
4y - 3 = 6
Add 3 to both sides:
4y = 9
Finally, divide by 4:
y = 9/4 or 2.25
So, the solution to this equation is y = 2.25.
2. -5(-2(x - 1) - (x + 1)) = 9
Begin by simplifying the expression inside the parentheses:
-5[-2x + 2 - x - 1] = 9
Further simplify:
-5[-3x + 1] = 9
Distribute the -5:
15x - 5 = 9
Add 5 to both sides:
15x = 14
Divide by 15:
x = 14/15 or 0.93
Thus, the solution to this equation is x = 0.93.
3. 0.08n - 0.09(n - 2) = 5 - 0.08
To begin, distribute the -0.09:
0.08n - 0.09n + 0.18 = 5 - 0.08
Combine like terms:
-0.01n + 0.18 = 4.92
Subtract 0.18 from both sides:
-0.01n = 4.74
Divide by -0.01:
n = 4.74 / -0.01
n = -474
Therefore, the solution to this equation is n = -474.
4. -2(3 - (x - 1) + 3x) + 2(x - 3 - 5(x - 3) - x) = 10
Begin by simplifying the expression inside each set of parentheses:
-2[3 - x + 1 + 3x] + 2[x - 3 - 5x + 15 - x] = 10
Further simplify:
-2[4x + 4] + 2[-5x + 12] = 10
Distribute the coefficients:
-8x - 8 - 10x + 24 = 10
Combine like terms:
-18x + 16 = 10
Subtract 16 from both sides:
-18x = -6
Divide by -18:
x = (-6) / (-18)
Simplifying, we have:
x = 1/3 or approximately 0.33
Thus, the solution to this equation is x = 1/3 or approximately 0.33.
I hope this breakdown helps you understand the steps involved in solving these equations. Let me know if you have any further questions.