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.

-5y - 7 = \( \frac{y}{7} \)
7 x (-5y - 7) = y
(7 x -5y) + (7 x -7) = y
-35y - 49 = y
-35y - 49 - y = 0
-35y - y = 49
-36y = 49
y = \( \frac{49}{-36} \)
y = -1\(\frac{13}{36}\)

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.

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{6}{2} \)
r = 3
a = πr²
a = π(3²)
a = 9π

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.

-8z - 4 < \( \frac{z}{-7} \)
-7 x (-8z - 4) < z
(-7 x -8z) + (-7 x -4) < z
56z + 28 < z
56z + 28 - z < 0
56z - z < -28
55z < -28
z < \( \frac{-28}{55} \)
z < -\(\frac{28}{55}\)

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:

x² - 3x + 0 = -2x + 2
x² - 3x + 0 - 2 = -2x
x² - 3x + 2x - 2 = 0
x² - x - 2 = 0

Next, factor the quadratic equation:

x² - x - 2 = 0
(x + 1)(x - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x - 2) must equal zero:

If (x + 1) = 0, x must equal -1
If (x - 2) = 0, x must equal 2

So the solution is that x = -1 or 2