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 - 2 < -3 - 3z
-7z < -3 - 3z + 2
-7z + 3z < -3 + 2
-4z < -1
z < \( \frac{-1}{-4} \)
z < \(\frac{1}{4}\)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

When solving an equation with two variables, 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.)

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² + 2x - 48 = 0
(x - 6)(x + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 6) or (x + 8) must equal zero:

If (x - 6) = 0, x must equal 6
If (x + 8) = 0, x must equal -8

So the solution is that x = 6 or -8

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)