0
In solving inequalities, you use many of the same steps as in equations. However, a few additional considerations apply. For example, care must be take when multiplying or dividing the inequality - if you multiply with a negative number, the direction of the inequality is reversed.
Example: -x < -2x + 15 -3x < 15 x > -5 Note that the "less than" was replaced with a "greater than" in the last step!
When multiplying or dividing by a variable (or by a variable expression), you may have to separately consider both cases: that the variable is positive, and that it is negative.
Add your answer:
Earn +20 pts
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
Explain how solving inequalities is alike and different from solving equations?
Most of the steps are the same. The main difference is that if you multiply or divide both sides of an inequality by a NEGATIVE number, you must change the direction of the inequality sign (for example, change "less than" to "greater than").
What are the differences between solving equations and solving inequalities?
One important difference is that if you multiply or divide both sides by a negative number, you need to invert the inequality sign. Example: -2x > 5 Dividing both sides by (-2): x < -2.5 Note that the greater-than sign changed to a less-than sign, because of the multiplication by a negative number.
What is the difference between a compound inequality using the word and and compound inequality using the word or?
The difference between them is that when solving an "and" inequality you are comparing two inequalities and when you are solving an "or" inequality you dont compare, you only use one inequality example of "and" . 2<x+3<7 example of "or" . 4<d or m<1
What is a method for solving a system of linear equations in which you multiply one or both equations by a number to get rid of a variable term?
It is called solving by elimination.
How are the rules for solving inequalities similar to those for solving equations?
Solving inequalities and equations are the same because both have variables in the equation.
What is one important difference between solving equations and solving inequalities?
One important difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, then the direction of the inequality must be reversed, i.e. "less than" becomes "greater than", and "less than or equal to" becomes "greater than or equal to".Actually, from a purist's sense, the reversal rule also applies with equations. Its just that the reversal of "equals" is still "equals". The same goes for "not equal to".
Why is it important to know various techniques for solving systems of equations and inequalities?
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
Why should you clear fractions when solving liner equations and inequalities?
it often simplifies arithmetic
What is the Bogomol'nyi bound?
Bogomol'nyi-Prasad-Sommerfield bound is a series of inequalities for solutions. This set of inequalities is useful for solving for solution equations.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
Why should you clear decimals when solving linear equations and inequalities?
It makes it allot less confusing. But, that is just my opinion.
How do you study for algebra 1 finals?
Study everything - that's your best bet. Important subjects probably include: Polynomials, Exponents, Radicals, Solving Equations, Solving Inequalities, Absolute Value Equations and Inequalities, Lines, Word Problems, Systems of Equations (2x2's), Factoring, Division of Polynomials, Quadratics, Parabolas, Complex Numbers, Algebraic Fractions, Functions
You know that equations and inequalities have different solution symbols, therefore, how many solutions will each one of them have when solving for the variable?
50
What are the steps to solving equations and inequalities?
Just keep doing the same thing to both sides of the equation at every step.
What are some differences between equations and inequalities?
The main difference is that when solving inequalities, if you multiply or divide by a negative number you have to be careful, since you then also have to switch the sign (for example, change a "less-than" sign to a "greater-than" sign). If you multiply or divide by an expression that contains a variable, you have to consider the two cases: that such an expression might be positive, or that it might be negative.
Explain how solving inequalities is alike and different from solving equations?
Most of the steps are the same. The main difference is that if you multiply or divide both sides of an inequality by a NEGATIVE number, you must change the direction of the inequality sign (for example, change "less than" to "greater than").
