Algebra Know-It-ALL
If the quantity by which we divide through is 0, we get undefined results on both sides of the inequality symbol. If the quantit ...
186 Equations and Inequalities We can divide both sides of a “strictly smaller than” statement by the same positive quantity and ...
We can divide both sides of a “larger than or equal” statement by the same positive quantity and get another valid statement. If ...
188 Equations and Inequalities If q= 0, then we end up with 0 ≤ 0, which is true. If the quantity by which we multiply the state ...
You must be careful if you multiply or divide an inequality through by a variable, or by any expression containing a variable. S ...
190 Equations and Inequalities We can say this in a more intuitive way by turning it around and reversing the sense of the inequ ...
In terms of an inequality statement and set notation, describe how the rational numbers relate to the irrational numbers. Here’ ...
192 CHAPTER 12 First-Degree Equations in One Variable Algebra involves the manipulation of equations or inequalities to find the ...
In this equation, c does not stand for the speed of light, and e doesn’t mean the exponential constant. All five constants are m ...
194 First-Degree Equations in One Variable Are you confused? If you aren’t sure how the five solutions come out of the five orig ...
Here’s a challenge! Manipulate the following equation so it contains x all by itself on the left side, and an expression contain ...
196 First-Degree Equations in One Variable The right-hand distributive law for division over addition, applied to the expression ...
Products and Ratios 197 Table 12-6. Process for solving the equation 4x= 0. Statements Reasons 4 x= 0 This is the equation we ar ...
198 First-Degree Equations in One Variable Here’s a challenge! Manipulate the following equation so it contains x all by itself ...
a− 8 x=b − 6 a+ 3 x= 12 b 6 a− 3 x/(bc)=− 24 d These seven equations can all be rearranged with the morphing laws we already kno ...
200 First-Degree Equations in One Variable Table 12-13. Streamlined process for solving the equation a− 3 x= 0. Statements Reaso ...
Standard form Whenever you encounter an equation that can be morphed into the following form, then that equation is a first-degr ...
202 First-Degree Equations in One Variable where k is a constant. Can this be rearranged into standard first-degree equation for ...
If you reverse the sense of the equation, you have 0 x= 4 Now you can subtract 4 from each side, getting 0 x− 4 = 0 It’s temptin ...
204 First-Degree Equations in One Variable Problem B The old Widow Johnson sold all her property and put the cash into a savings ...
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