For what values of x will the angle be acute? (2x-6)degrees
To determine the values of x for which the angle is acute, we need to find the range of values that make the angle measure less than 90 degrees.
An acute angle is defined as an angle with a measure between 0 degrees and 90 degrees.
So, we need to solve the inequality:
0 < (2x - 6) < 90
Let's solve it step by step:
1. Add 6 to all parts of the inequality:
0 + 6 < (2x - 6) + 6 < 90 + 6
6 < 2x < 96
2. Divide all parts of the inequality by 2:
6/2 < 2x/2 < 96/2
3 < x < 48
Therefore, the values of x that make the angle acute are x > 3 and x < 48.
To determine the values of x for which the angle (2x-6) degrees will be acute, we need to understand what it means for an angle to be acute.
An acute angle is an angle that measures less than 90 degrees. So, we need to find the values of x that make the expression (2x-6) degrees less than 90 degrees.
To solve this, we set up the inequality:
(2x-6) < 90
Now, we can solve for x by isolating it on one side of the inequality. Let's do that step-by-step:
1. Add 6 to both sides of the inequality to eliminate the negative 6:
2x < 90 + 6
Simplifying the right side of the inequality:
2x < 96
2. Divide both sides of the inequality by 2 to isolate x:
x < 96/2
Simplifying the right side of the inequality:
x < 48
Therefore, for the angle (2x-6) degrees to be acute, x must be less than 48.
In conclusion, the values of x that will result in an acute angle are any real numbers less than 48.
An acute angle is less than 90°
So, 2x-6 < 90
2x < 96
x < 48