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.

6a⁷ - 7a⁷ = -1a⁷

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.

-2z - 8 = 5 - 4z
-2z = 5 - 4z + 8
-2z + 4z = 5 + 8
2z = 13
z = \( \frac{13}{2} \)
z = 6\(\frac{1}{2}\)

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.

3c - 4 > \( \frac{c}{-1} \)
-1 x (3c - 4) > c
(-1 x 3c) + (-1 x -4) > c
-3c + 4 > c
-3c + 4 - c > 0
-3c - c > -4
-4c > -4
c > \( \frac{-4}{-4} \)
c > 1

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

AD = AB + BD

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

z² + 3z - 37 = 2z + 5
z² + 3z - 37 - 5 = 2z
z² + 3z - 2z - 42 = 0
z² + z - 42 = 0

Next, factor the quadratic equation:

z² + z - 42 = 0
(z - 6)(z + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 6) or (z + 7) must equal zero:

If (z - 6) = 0, z must equal 6
If (z + 7) = 0, z must equal -7

So the solution is that z = 6 or -7