220 algebra De mystif ieD
Summary
In this chapter, we learned how to• Use PEMDAS to compute complex expressions. The letters in PEMDAS indi-
cate the order of operations. The “P” stands for “parentheses.” We work
inside parentheses first. The “E” stands for “exponents.” We compute expo-
nents second. The “M” stands for “multiplication” and “D” stands for “divi-
sion.” We multiply and divide third, working from left to right. Finally, “A”
stands for “addition” and “S” stands for subtraction. We add and subtract
last, working from left to right.
• Solve linear equations. To solve an equation for x (or some other variable)
means to isolate x on one side of the equation. Our strategy is to simplify
each side of the equation and then use addition/subtraction to collect
terms having x in them on one side of the equation and terms without x
on the other side. In the last step, we divide each side of the equation by
the coefficient of x.
• Solve equations having fractions/decimals in them by clearing the fractions/
decimals. If the equation has fractions, we identify the LCD and multiply each
side of the equation by the LCD. This eliminates the fraction(s). If the equa-
tion has decimal numbers, we multiply both sides of the equation by a power
of 10 large enough to eliminate any decimal. We then proceed as above.
• Solve formulas containing multiple variables for one of the variables. We use the
same strategy as above to solve equations containing multiple variables—
simplify each side of the equation and then collect the terms having the
variable we want on one side and terms without this variable on the other
side and then divide each side of the equation by the coefficient of this
variable. The coefficient probably contains another variable.
• Solve equations leading to linear equations. If the equation contains a variable
underneath a square root symbol (radical), we isolate the root symbol on one
side of the equation and then square both side of the equation. This elimi-
nates the root. We then solve the remaining equation using the strategy
outlined above. If the equation contains a rational expression (a fraction
having a variable in the numerator/denominator), we use one of two strate-
gies. For equations in the form “fraction = fraction,” we cross-multiply. That
is, we multiply each numerator by the denominator of the other fraction and
then solve the equation. For other equations, we identify the LCD and mul-
tiply each side by the LCD, which eliminates the fractions.