Identify the range of values for y.

The figure shows a triangle. The first side of the triangle goes from the lower left corner to the upper right corner. The second side of the triangle goes from the lower right corner to the upper left corner. An angle between these sides is an obtuse angle. The third side of the triangle goes from the lower left corner to the lower right corner. A line connects a vertex of the obtuse angle with a point on the third side. This line divides the third side into left and right segments. An angle between this line and the second side measures 60 degrees. An angle between this line and the left segment of the third side measures 105 degrees. The second side of the triangle is congruent to the left segment of the third side. The right segment of the third side has a length of 5 times y plus 8 units. The first side of the triangle has a length of 4 times y plus 15 units.

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MrRoyal MrRoyal · Answer 1 · 2022-07-24T19:59:44+02:00

The range of values of y is -1.6 < y < 7

The complete question is added as an attachment

From the attached image, we have the following sides

4y + 15 and 5y + 8

Both sides must be greater than 0.

So, we have:

4y + 15 > 0 and 5y + 8 > 0

Rewrite as:

4y > -15 and 5y > - 8

Solve for y

y > -3.75 and y > -1.6

If y is less than -1.6, the side 5y + 8 would be negative.

So, we make use of the inequality y > -1.6 as one of the range

Also, 4y + 15 is greater than 5y + 8.

So, we have:

4y + 15 > 5y + 8

Evaluate the like terms

-y > -7

Divide by -1

y < 7

So, we have:

y > -1.6 and y < 7

Combine both inequalities

-1.6 < y < 7

Hence, the range of values of y is -1.6 < y < 7