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.

5z - 7 > \( \frac{z}{3} \)
3 x (5z - 7) > z
(3 x 5z) + (3 x -7) > z
15z - 21 > z
15z - 21 - z > 0
15z - z > 21
14z > 21
z > \( \frac{21}{14} \)
z > 1\(\frac{1}{2}\)

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.

8a + 8a = 16a

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -27 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -9 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 6y - 27
y² + (-9 + 3)y + (-9 x 3)
(y - 9)(y + 3)

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 9 x 5
a = 45

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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

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 = 1² + 1²
c² = 2
c = \( \sqrt{2} \)