The first step is to find the zeros of the polynomial x2 - x - 6. We are looking for values of x where the polynomial is negative.
Equations and Inequalities Involving Signed Numbers In chapter 2 we established rules for solving equations using the numbers of arithmetic. Now that we have learned the operations on signed numbers, we will use those same rules to solve equations that involve negative numbers.
We will also study techniques for solving and graphing inequalities having one unknown. Example 1 Solve for x and check: Then follow the procedure learned in chapter 2.
Identify a literal equation. Apply previously learned rules to solve literal equations. An equation having more than one letter is sometimes called a literal equation.
It is occasionally necessary to solve such an equation for one of the letters in terms of the others. The step-by-step procedure discussed and used in chapter 2 is still valid after any grouping symbols are removed.
Example 1 Solve for c: At this point we note that since we are solving for c, we want to obtain c on one side and all other terms on the other side of the equation.
Thus we obtain Remember, abx is the same as 1abx. We divide by the coefficient of x, which in this case is ab.
Compare the solution with that obtained in the example. Sometimes the form of an answer can be changed. In this example we could multiply both numerator and denominator of the answer by - l this does not change the value of the answer and obtain The advantage of this last expression over the first is that there are not so many negative signs in the answer.
EXAMPLE 1 Writing Inequalities Write the word sentence as an inequality. a. A number c is less than 4. A number c is less than 4. c Writing and Graphing Inequalities Solve the equation. Check your solution. x + 3 = 12 x − 6 = 8 16 + x = 44 Write and solve an inequality for the following: three-fourths of a number is greater than or equal to Sep 01, · Goal: You will be able to write inequalities, graph inequalities on a number line, and solve one-step inequalities. Goal: You will be able to write inequalities, graph inequalities .
Multiplying numerator and denominator of a fraction by the same number is a use of the fundamental principle of fractions. The most commonly used literal expressions are formulas from geometry, physics, business, electronics, and so forth. Example 4 is the formula for the area of a trapezoid.
A trapezoid has two parallel sides and two nonparallel sides. The parallel sides are called bases. Removing parentheses does not mean to merely erase them. We must multiply each term inside the parentheses by the factor preceding the parentheses. Changing the form of an answer is not necessary, but you should be able to recognize when you have a correct answer even though the form is not the same.
Example 5 is a formula giving interest I earned for a period of D days when the principal p and the yearly rate r are known.Exercise Set Interval Notation and Linear Inequalities 94 University of Houston Department of Mathematics For each of the following inequalities: (a) Write the inequality algebraically.
Solving and Graphing Inequalities What is the answer to the following questions? 5 = 16, the only solution is x = 7. When we have an inequality to solve, we have a range of numbers that can be a solution.
In that range there is an infinite amount of possible numbers that make the inequality true. Write an inequality that represents: 6. We can solve the inequality $(x-a)(x-b) >0$ by determining the sign of each factor on the three pieces.
We can take a similar approach for inequalities with more than two factors. In this case, the line gets split into more pieces, however the approach is the same.
How do you write and solve an inequality represents the values of x for which the area of the rectangle will be at least 35 square feet?
Seven less than the product of twice a number is greater than 5 more an the same number. Solve word problems leading to inequalities of the form px + q > r or px + q inequality and interpret it .
absolute value equations and inequalities, which will give them greater insight into the solution process. Method 1: Graphing. 2. Ask students to graph. y x. 2 3. and. y. 5. Then, solve, write the solution set in set-builder notation, and graph the solution set on a number line.