A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

2z + 7 > \( \frac{z}{-2} \)
-2 x (2z + 7) > z
(-2 x 2z) + (-2 x 7) > z
-4z - 14 > z
-4z - 14 - z > 0
-4z - z > 14
-5z > 14
z > \( \frac{14}{-5} \)
z > -2\(\frac{4}{5}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-a - 9 = \( \frac{a}{7} \)
7 x (-a - 9) = a
(7 x -a) + (7 x -9) = a
-7a - 63 = a
-7a - 63 - a = 0
-7a - a = 63
-8a = 63
a = \( \frac{63}{-8} \)
a = -7\(\frac{7}{8}\)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 5² + 5²
c² = 25 + 25
c² = 50
c = \( \sqrt{50} \)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with c° = 18, the value of z° is 18.