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How do you differentiate between an expression and an equation? Provide an example of each, where the two are either related to or similar to each other. (6/26)
The major difference between an equation and an expression is that while an equation has to be solved, an expression does not. For instance, this is an equation: 3x + 1 = 5.if x is multiplied by 3 and add 1, the result will be a 5. In similar vein, an equation consists of two expressions connected by an equals sign. It can only be true or false (Miller, 2009). The primary difference between the two is an equal sign.
References: Miller, M. (2009). Algebra: Book 3. Eugene, OR: Garlic Press. Answer to Nathan: (6/26) Hi Nathan, I agree with you when you say "an expression is a mathematical "phrase". " In most cases it stands for a single element. 3x + 1 is an example of an expression. The expression means that its value three times the value of x, plus 1. An expression can also be a single number or variable, since those have a numerical value. Unlike in the case of an equation, an expression is never true or false, but just has a numerical value.

Are the properties used to solve inequalities the same as those used to solve equations? Explain your answer. (6/27)
The properties to solve inequalities are NOT exactly the same as the properties to solve equations. But, the properties to solve equations ARE exactly like those used to solve inequalities. Inequalities have an exclusive property while solving because of the character of the comparability of the inequality. The exclusive property is the function of multiplying or dividing by a minus integer. By multiplying or dividing by a minus integer, the comparability of the inequality is changed. In case rendered the same, this would develop a wrong expression. The additional property in solving inequalities is that whenever multiplying or dividing by a minus integer, the comparison should be changed. Answer to LauraWynn: (6/27)
An illustration would be:
-2x > 4
In solving this, you would be required to divide by -2 to both sides of the inequality. If you do this, it generates the wrong expression: x > -2 When dividing, or multiplying, by a minus integer, the comparison should be changed. For example: x < -2
The same holds true while multiplying an inequality by a minus integer. x/-2 < 1/2 = x > -1 Answer to Maribel
It is worthy to note that whereas equations have one solution, inequalities have several solutions. For equations such as x = 5, there is only one possible value for x (5), but for the inequality x > 5, there are an infinite number of possible values for x such as 5.01, 6, 102.7, etc. To solve the inequality, isolate the variable on one side using transformations which produce equivalent inequalities. Properties that can be applied to equations can also be applied to inequalities (Miller, 2009).
References: Miller, M. (2009). Algebra: Book 3. Eugene, OR: Garlic Press. How might you graph an equation in two variables in the rectangular coordinate system? (6/28)
A rectangular coordinate system is formed by two perpendicular number lines that intersect at the point corresponding to the number 0 on each line. This point of intersection is called the origin and is denoted by the symbol O. The horizontal and vertical number lines are called the x-axis and the y-axis, respectively. These axes divide the plane into four regions, called quadrants, which are numbered as shown below.

What is the slope of a line? Identify the possible values of the slope and the relation to the line they pass through. For example, if the slope of a line is 3 / 2, it means that the rise is 3, the run is 2, and the line rises from left to right. (6/28)
The slope is the rate of change (steepness of line). Slope is also termed as ratio of rise above run.The slope of the line is calculated by dividing the difference of the y-coordinates of a point on a line by the difference of the x-coordinates. The formula is as shown below. For this reason, if the slope is 3⁄2 then the equation will be 3⁄2 = (Y_2-Y_1)⁄(X_2-X_1 )
Hence, if we had the values of one of the coordinates, we would possibly calculate the value of the other coordinate.

Answer to Kenneth
Great Post! One of the most important properties of a straight line is in how it angles away from the horizontal. This is what is commonly referred to as the slope of the line. To calculate the slope of a line, one needs two points on that line (Seber & Lee, 2012). The greater the slope of the line the steeper the line will be. The slope of a line characterizes the general direction in which a line points.
Seber, G. A. F., & Lee, A. J. (2012). Linear Regression Analysis. Hoboken: Wiley.

Answer to Laura
The methods used to solve an equation are closely similar to the ones used to solve an inequality. Nevertheless, the major difference is that different additive and multiplicative properties apply. When solving an equation, the variables are isolated by applying algebraic properties. This ensures that when equations are being solved, the equation is kept in balance. The solution to an inequality is a value that makes the equation true. This also applies to an inequality.

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