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.

7z + 6 < \( \frac{z}{-5} \)
-5 x (7z + 6) < z
(-5 x 7z) + (-5 x 6) < z
-35z - 30 < z
-35z - 30 - z < 0
-35z - z < 30
-36z < 30
z < \( \frac{30}{-36} \)
z < -\(\frac{5}{6}\)

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.

8a + 6 < 9 - 2a
8a < 9 - 2a - 6
8a + 2a < 9 - 6
10a < 3
a < \( \frac{3}{10} \)
a < \(\frac{3}{10}\)

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

c² = a² + b²
c² = 9² + 7²
c² = 81 + 49
c² = 130
c = \( \sqrt{130} \)

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, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

3a(a - x)
3(9)(9 - 2)
3(9)(7)
(27)(7)
189