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.

5a⁸ - 4a⁸ = 1a⁸

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 - 1 > \( \frac{z}{7} \)
7 x (-5z - 1) > z
(7 x -5z) + (7 x -1) > z
-35z - 7 > z
-35z - 7 - z > 0
-35z - z > 7
-36z > 7
z > \( \frac{7}{-36} \)
z > -\(\frac{7}{36}\)

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(8 + 9)(5)
a = ½(17)(5)
a = ½(85) = \( \frac{85}{2} \)
a = 42\(\frac{1}{2}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with b° = 149, the value of a° is 31.

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:

y² + 2y - 28 = -4y - 1
y² + 2y - 28 + 1 = -4y
y² + 2y + 4y - 27 = 0
y² + 6y - 27 = 0

Next, factor the quadratic equation:

y² + 6y - 27 = 0
(y - 3)(y + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 3) or (y + 9) must equal zero:

If (y - 3) = 0, y must equal 3
If (y + 9) = 0, y must equal -9

So the solution is that y = 3 or -9