I don’t understand question 42,43

42. x = 25

43. LM = 11

Step-by-step explanation:

For 42, the three angles of a triangle, when added, = 180 degrees. We know that one of the angles is 90 degrees...a right angle.

So: 90 + 2x + x + 15 = 180

105 + 3x = 180

3x = 75

x = 25

If they ask for more information: the three angles are 90 degrees, 50 degrees (2x), and 40 (x + 15). 90 + 50 + 40 = 180

For 43, ray PN bisects (cuts in equal halves) the triangle. We know this because the two segments LP and PM are equal. As a result, the triangles LPM and PNM are mirror images. Since MN = 11, LM also = 11.

Please let me know if you have questions.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal