Can someone please show me how to solve these problems step-by-step so that I can understand how to do them?
1.Use inverse operations to write a related inequality and solve for the variable:
d/6 < 12
2.Use inverse operations to solve the inequality:
m-27=85
3.Use transformations to solve the equation:
2.5 (6+k)=3k
4.Use transformations to solve the inequality:
19-3m+5+7m < 0
Basically I don't get transformations and inverse operations. Pleeasee help! THANKS A MILLION =)
-MC
remember the inverse operation of multiplication is division and vice versa
and the inverse operation of addition is subtraction and vice versa
so in #1 ,
d/6 < 12 , we have a division by 6, so the inverse is multiplication by 6
so multiply both sides by 6
d < 72
in #2
m-27 = 85
m - 27 + 27 = 85 + + 27
m = 112
looks like a big deal is made about nothing
using "transformations" to solve such trivial questions as #3 and #4 ????
Why not just go ahead and solve it ?
Ummm OK thanks; I think I have a couple more questions coming up...
-MC
Josh is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges and allows unlimited mileage.
Company B has an initial fee of and charges an additional for every mile driven.
For what mileages will Company A charge less than Company B?
Use for the number of miles driven, and solve your inequality for .
Sure, I'll be happy to help you understand how to solve each of these problems step-by-step.
1. Use inverse operations to write a related inequality and solve for the variable:
Given: d/6 < 12
To solve for d, we want to isolate it on one side of the inequality.
First, we can multiply both sides of the inequality by 6 to get rid of the fraction:
(d/6) * 6 < 12 * 6
d < 72
So the related inequality is d < 72. This means that any value less than 72 would satisfy the original inequality.
2. Use inverse operations to solve the inequality:
Given: m - 27 = 85
To solve for m, we want to isolate it on one side of the equation.
First, we can add 27 to both sides of the equation to move the constant term to the other side:
m - 27 + 27 = 85 + 27
m = 112
So the solution to the inequality is m = 112.
3. Use transformations to solve the equation:
Given: 2.5(6 + k) = 3k
To solve for k, we want to isolate it on one side of the equation.
First, we can distribute the 2.5 to eliminate the parenthesis:
2.5 * 6 + 2.5 * k = 3k
15 + 2.5k = 3k
Next, we can subtract 2.5k from both sides to move the variable terms to one side:
15 + 2.5k - 2.5k = 3k - 2.5k
15 = 0.5k
Finally, we can divide both sides of the equation by 0.5 to solve for k:
15 / 0.5 = k
k = 30
So the solution to the equation is k = 30.
4. Use transformations to solve the inequality:
Given: 19 - 3m + 5 + 7m < 0
To solve for m, we want to isolate it on one side of the inequality.
First, we can combine like terms:
24 + 4m < 0
Next, we can subtract 24 from both sides to move the constant term to the other side:
24 + 4m - 24 < 0 - 24
4m < -24
Finally, we can divide both sides of the inequality by 4 to solve for m:
(4m) / 4 < (-24) / 4
m < -6
So the solution to the inequality is m < -6.
I hope this helps you understand how to solve these problems using inverse operations and transformations. Let me know if you have any further questions!