4(r-7)+2>5(r+3)-28
I tend to make things too difficult.. can someone please check my answer?
{r l r > 31/4}
4(r-7)+2>5(r+3)-28
4r - 28 > 5r + 15 - 28
-r > 15
r < -15
I think Reiny lost the +2 on the left...
4r-28+2>5r+15-28
-r>13
r<-13
I missed the +2
Let's try again
4(r-7)+2>5(r+3)-28
4r - 28 + 2 > 5r + 15 - 28
-r > 15 - 2
r < -13
thank you so much... I tend to make things too difficult I don;t know why I do this.. and the extra number and letters throw me off... thank you I will use this tip for further references... appreciate it so much
To solve the inequality 4(r-7)+2 > 5(r+3)-28, we need to simplify and isolate the variable r.
Let's start by simplifying both sides of the inequality:
4(r-7)+2 > 5(r+3)-28
4r - 28 + 2 > 5r + 15 - 28
4r - 26 > 5r - 13
Next, we want to isolate the variable r on one side of the inequality. To do this, we'll move the terms involving r to one side and the constant terms to the other side:
4r - 5r > -13 + 26
-r > 13
Note: Since we are dividing both sides by -1, we need to reverse the inequality sign.
Now, let's divide both sides by -1:
-r / -1 < 13 / -1
r < -13
So, the solution to the inequality is r < -13.
Now, let's check the answer {r | r > 31/4}:
The expression {r | r > 31/4} represents the set of all values of r greater than 31/4, which is equivalent to r > 7.75.
The answer you provided, r < -13, does not satisfy the condition r > 7.75, so it does not match the solution to the inequality. Therefore, the answer {r | r > 31/4} is incorrect.
To double-check our solution, we can substitute a value less than -13 into the original inequality to see if it holds true. Since r < -13, let's choose r = -14:
4(-14-7)+2 > 5(-14+3)-28
-56 + 2 > -55 - 28
-54 > -83
This inequality holds true, so the solution r < -13 is correct.