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.

6z + 5 < \( \frac{z}{2} \)
2 x (6z + 5) < z
(2 x 6z) + (2 x 5) < z
12z + 10 < z
12z + 10 - z < 0
12z - z < -10
11z < -10
z < \( \frac{-10}{11} \)
z < -\(\frac{10}{11}\)

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 6cm + 8cm + 8cm = 22cm

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 2)
c = 4π

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

9a - 5a = 4a