can some one solve this
Ex 1:
-2x+7>22
-2x+7-7>22-7
-2x>15
-2x/(-2)<15/(-2) Switching the order of the inequality here is essential to keep the solutions true for the inequality since I divided by a negative #.
x<-7.5
Check:
Try -8. It should work since it is less than -7.5
-2x+7>22
-2(-8)+7>22
16+7>22
23>22
It does make the inequality true so it looks as if I have solved correctly. So my solution is {x|x<-7.5} which is just a mathy notation way of saying "the set of all values for x such that x is less than -7.5.” This notation amplifies that this is a whole set of values that x can equal and not just one value.
You forgot to reverse the carat, when dividing by -2.
x > -7.5
It seems that you have already solved the inequality correctly. To explain the steps in solving the inequality -2x + 7 > 22:
1. Start by isolating the variable x. Subtract 7 from both sides of the inequality:
-2x + 7 - 7 > 22 - 7
-2x > 15
2. Since -2 is multiplied by x, we need to divide both sides of the inequality by -2. When dividing by a negative number, it is essential to switch the direction of the inequality to maintain the solutions true. So, divide both sides by -2:
-2x / -2 < 15 / -2
x < -7.5
By following these steps, you found that the value of x is less than -7.5. To check if this solution is correct, substitute a value that is less than -7.5 back into the original inequality to see if it holds true. In this case, you used x = -8:
-2(-8) + 7 > 22
16 + 7 > 22
23 > 22
Since 23 is greater than 22, the inequality holds true. Therefore, the solution is correct. In set notation, you can represent the solution as {x | x < -7.5}, which means "the set of all values for x such that x is less than -7.5".