Solving Algebraic Equations for “x”
• Goal of solving equations is to determine the value of the missing value, commonly known as x. Therefore, you need to eliminate the values that are attached to x, using inverse operations and the property of equality to get x by itself.
• Property of Equality
o The property of equality is used to solve equations for the missing value, commonly known as a variable.
o Remember, when solving equations, do the same thing to both sides of an equation.
o For example, if you add 5 to one side of an equation to eliminate the 5 that is being subtracted from x, then be sure to add 5 to the other side of the equation.
o Again, if you divide one side of the equation by 3 to eliminate the 3 that is being multiplied by x, then be sure to divide the other side of the equation by 3.
• Inverse Operations
o Addition and Subtraction are inverse operations
o Multiplication and Division are inverse operations
o Squaring and Square Roots are inverse operations
• Checking your work
o When solving equations, it is very easy to ensure that your answer is correct – simply substitute the value in place of the variable to be sure that both sides of the equation equal.
• The word percent means “per hundred.”
• To determine the percent of a value, the easiest way is to change the percent into a decimal, and then multiply the value times the decimal.
• Since percent means per hundred, remember that to change a percent to a decimal, we divide by one hundred. Examples include:
45% = .45
60 % = .60
5% = .05
• Solving proportions can be easily understood by recognizing that a proportion is the comparison of two equal ratios (or equal fractions).
• Set up a proportion as two equal fractions, ensuring that the two top numbers are values representing the same units, and the bottom numbers are values representing the same units. If the proportion is set up correctly, then one of the four values represents the missing value. Cross multiply to set up an equation, and then solve for x. For example, if Jake can text 87 words in three minutes, how many words can he text in five minutes? In this example, the equation of two equal ratios (or fractions) would look like: 87/3 = x/5 Then, cross multiply and solve for x.
• Combining like terms (adding and subtracting polynomials)
o Like terms are algebraic terms that have the same variable and same exponent. If they are alike, the coefficients of the terms can be combined (by either adding or subtracting).
• Multiplying Polynomials
o FOIL is an acronym for First, Outer, Inner, Last when multiplying two binomials together.