An acute angle measure (6x-45). Write an inequality to describe the range of all possible values of x?
6x-45 < 90, since acute angles are less than 90°.
Solving this:
6x < 90 + 45
6x < 135
x < 22.5
acute means less than 90º
0 < (6x - 45) < 90
Oops! I made a mistake. R_scott is right. I forgot the lower range... of course an angle has to be greater than 0°...
Thus, the correct range is 0 < x < 22.5
Another mistake on my behalf: 7.5 < x < 22.5 should be right.
To determine the range of all possible values of x for an acute angle measure given by the expression (6x-45), we need to consider the definition of an acute angle, which is an angle that measures less than 90 degrees.
To write an inequality to describe the range of all possible values of x, we can start by creating the inequality based on the given expression. The angle measure (6x-45) must be less than 90 degrees, so the inequality will be:
6x - 45 < 90
Now, let's solve this inequality to find the range of possible values for x:
Add 45 to both sides of the inequality to isolate the term with x:
6x - 45 + 45 < 90 + 45
Simplify:
6x < 135
Finally, divide both sides of the inequality by 6 to solve for x:
6x/6 < 135/6
Simplify:
x < 22.5
Therefore, the range of all possible values of x for an acute angle measure (6x-45) is x < 22.5.