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(5 + 6)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22

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.

-6b + 3 < \( \frac{b}{-2} \)
-2 x (-6b + 3) < b
(-2 x -6b) + (-2 x 3) < b
12b - 6 < b
12b - 6 - b < 0
12b - b < 6
11b < 6
b < \( \frac{6}{11} \)
b < \(\frac{6}{11}\)

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:

a² + 18a + 41 = 4a - 4
a² + 18a + 41 + 4 = 4a
a² + 18a - 4a + 45 = 0
a² + 14a + 45 = 0

Next, factor the quadratic equation:

a² + 14a + 45 = 0
(a + 5)(a + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 5) or (a + 9) must equal zero:

If (a + 5) = 0, a must equal -5
If (a + 9) = 0, a must equal -9

So the solution is that a = -5 or -9

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

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.

6x - 4 > -6 - 4x
6x > -6 - 4x + 4
6x + 4x > -6 + 4
10x > -2
x > \( \frac{-2}{10} \)
x > -\(\frac{1}{5}\)