A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

5a + 2z = 4a + 3z + 3
5a = 4a + 3z + 3 - 2z
5a - 4a = 3z + 3 - 2z
a = z + 3

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.

3b + 5 < \( \frac{b}{-4} \)
-4 x (3b + 5) < b
(-4 x 3b) + (-4 x 5) < b
-12b - 20 < b
-12b - 20 - b < 0
-12b - b < 20
-13b < 20
b < \( \frac{20}{-13} \)
b < -1\(\frac{7}{13}\)

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 - 7y - 44 = -5y + 4
y² - 7y - 44 - 4 = -5y
y² - 7y + 5y - 48 = 0
y² - 2y - 48 = 0

Next, factor the quadratic equation:

y² - 2y - 48 = 0
(y + 6)(y - 8) = 0

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

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

So the solution is that y = -6 or 8

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 3)
sa = 2π(36) + 2π(18)
sa = (2 x 36)π + (2 x 18)π
sa = 72π + 36π
sa = 108π