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 (c) on one side of the equation and put everything else on the other side.

5c + 2z = 4c + 3z + 3
5c = 4c + 3z + 3 - 2z
5c - 4c = 3z + 3 - 2z
c = 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.

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

a² - 7a - 44 = -5a + 4
a² - 7a - 44 - 4 = -5a
a² - 7a + 5a - 48 = 0
a² - 2a - 48 = 0

Next, factor the quadratic equation:

a² - 2a - 48 = 0
(a + 6)(a - 8) = 0

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

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

So the solution is that a = -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