Determine whether the given numbers are solutions of the inequality. y-8>2y-3
4, -11, -19, -1
(are any of these numbers a solution to the inequality?)
Given
y-8>2y-3 ... (1)
Find if 4, -11, -19, -1 are solutions to the inequality (1):
1. y=4
4-8>2(4)-3 ?
-4 > 5 ?
since -4<5, the answer is no, 4 is not a solution to (1)
2. y=-11
-11-8 > 2(-11)-3 ?
-19 > -25 ?
Draw this on the number line:
....-25......-19.......-1 0 1 2 3 4...
Since -19 is to the right of -25 on the number line, we conclude that yes, y=-11 is a solution to inequality (1).
Continue this way for the other two cases.
Post for checking if you wish.
To determine whether the given numbers are solutions of the inequality y - 8 > 2y - 3, we need to substitute each number into the inequality and check if the inequality holds true.
Let's start with the first number, 4:
Substituting 4 into the inequality, we get:
4 - 8 > 2(4) - 3
-4 > 8 - 3
-4 > 5
Since -4 is not greater than 5, the inequality does not hold true, meaning 4 is not a solution of the inequality.
Let's move on to the second number, -11:
Substituting -11 into the inequality, we get:
-11 - 8 > 2(-11) - 3
-19 > -22 - 3
-19 > -25
Since -19 is greater than -25, the inequality holds true, meaning -11 is a solution of the inequality.
Now let's try the third number, -19:
Substituting -19 into the inequality, we get:
-19 - 8 > 2(-19) - 3
-27 > -38 - 3
-27 > -41
Again, since -27 is greater than -41, the inequality holds true, meaning -19 is a solution of the inequality.
Finally, let's check -1:
Substituting -1 into the inequality, we get:
-1 - 8 > 2(-1) - 3
-9 > -2 - 3
-9 > -5
Once again, since -9 is greater than -5, the inequality holds true, meaning -1 is a solution of the inequality.
So, out of the given numbers, -11, -19, and -1 are solutions of the inequality, while 4 is not.
To determine if each number is a solution to the inequality y - 8 > 2y - 3, we will substitute each number for y and check if the inequality holds.
1. Substituting 4 for y:
4 - 8 > 2(4) - 3
-4 > 5
The inequality is FALSE.
2. Substituting -11 for y:
-11 - 8 > 2(-11) - 3
-19 > -25
The inequality is TRUE.
3. Substituting -19 for y:
-19 - 8 > 2(-19) - 3
-27 > -35
The inequality is TRUE.
4. Substituting -1 for y:
-1 - 8 > 2(-1) - 3
-9 > -1
The inequality is TRUE.
Therefore, among the given numbers, -11, -19, and -1 are solutions to the inequality y - 8 > 2y - 3.