Solve.
Just need to verify if I am right.
-25 ¡Ü 4x-8 ¡Ü-1
-17/4 ¡Ü x ¡Ü 7/4
Pleas use a standard symbol instead of ¡Ü
Are there supposed to be = or > < symbols somewhere?
It is better if you show your work; then we will tell you if it is right.
-25 ¡Ü 4x-8 ¡Ü-1
The solution is {x|-17/4 ¡Ü x ¡Ü 7/4
To solve the inequality -25 ≤ 4x - 8 ≤ -1, you need to isolate the variable x. Here's how you can do it:
1. Start by adding 8 to all parts of the inequality:
-25 + 8 ≤ 4x - 8 + 8 ≤ -1 + 8
-17 ≤ 4x ≤ 7
2. Next, divide all parts of the inequality by 4 (since the coefficient of x is 4):
-17/4 ≤ 4x/4 ≤ 7/4
-17/4 ≤ x ≤ 7/4
So, your solution is -17/4 ≤ x ≤ 7/4.
Now let's verify if your given solution of -17/4 ≤ x ≤ 7/4 is correct:
1. Plug in a value for x within this range and check if the inequality holds true. Let's use x = -2 (which is between -17/4 and 7/4).
-25 ≤ 4x - 8 ≤ -1
-25 ≤ 4(-2) - 8 ≤ -1
-25 ≤ -8 - 8 ≤ -1
-25 ≤ -16 ≤ -1 (True)
2. Now let's test a value outside the given range. Let's use x = 2, which is greater than 7/4.
-25 ≤ 4x - 8 ≤ -1
-25 ≤ 4(2) - 8 ≤ -1
-25 ≤ 8 - 8 ≤ -1
-25 ≤ 0 ≤ -1 (False)
Since the inequality is false when we use x = 2, which is outside the range -17/4 ≤ x ≤ 7/4, we can conclude that your given solution is correct: -17/4 ≤ x ≤ 7/4.