x + 3 > 7 and 3 + 7 > x
x > 4 and 10 > x
4 < x < 10
Replace the dimensions of the above figure with 12 ft and 18 ft and write the inequality for x.
To replace the dimensions of the figure with 12 ft and 18 ft, we can assume that one side of the figure is 12 ft and the other side is 18 ft. Since we are dealing with a figure, it is safe to assume that both the length and width of the figure are positive numbers.
The inequality for x can be derived from the two inequalities given initially:
4 < x < 10
Since x represents the length or width of the figure, we know that both the length and width must be greater than 4 ft and less than 10 ft.
To determine the inequality with the dimensions of 12 ft and 18 ft, we need to substitute those values into the inequality.
So, the inequality would be:
4 < x < 10
Now, substitute the value of 12 ft for either x (length or width) in the inequality:
4 < 12 < 10
This is not a valid inequality since it is not possible for a number to be greater than 10 and less than 4 at the same time. Therefore, the value of 12 ft cannot be a valid dimension for x in this case.
Similarly, substitute the value of 18 ft for either x (length or width) in the inequality:
4 < 18 < 10
Again, this is not a valid inequality since it is not possible for a number to be greater than 10 and less than 4 at the same time. Therefore, the value of 18 ft cannot be a valid dimension for x in this case.
Based on the given inequality, no valid value can be substituted for x if the dimensions of the figure are 12 ft and 18 ft.