Write an inequality for each problem

Step 3 Solve the resulting equation. Since 3,2 checks in both equations, it is the solution to the system. To put it mathematically: Identify a literal equation. What are the coordinates of the origin. Remember, we only need two points to determine the line but we use the third point as a check.

To eliminate x multiply each side of the first equation by 3 and each side of the second equation by If w is less thanit's going to be a negative number.

Solving Inequalities

This gives us a convenient method for graphing linear inequalities. Write your answer in a complete sentence. Step 3 If the point chosen is in the solution set, then that entire half-plane is the solution set. Second we know that if we add the same or equal quantities to both sides of an equation, the results are still equal.

This means the graphs of all systems in this chapter will intersect in a single point. Word Problem Solving Strategies Read through the entire problem. Example 2 Sketch the graph and state the slope of Solution Choosing values of x that are divisible by 3, we obtain the table Why use values that are divisible by 3.

Observe that when two lines have the same slope, they are parallel. But these things will change direction of the inequality: Graphs are used because a picture usually makes the number facts more easily understood.

Study them closely and mentally answer the questions that follow. Three times the first number added to five times the second number is 9.

Remember that the solution for a system must be true for each equation in the system. The set composed of rational and irrational numbers is called the real numbers. There are many types of graphs, such as bar graphs, circular graphs, line graphs, and so on.

Sometimes the form of an answer can be changed. The slope indicates that the changes in x is 4, so from the point 0,-2 we move four units in the positive direction parallel to the x-axis.

So this is the first part. Take special note of this fact. You could also substitute any number less than Many word problems can be outlined and worked more easily by using two unknowns. Highlight the important information and key words that you need to solve the problem. Look at both equations and see if either of them has a variable with a coefficient of one.

What don't you know. So, we must use the greater than or equal to symbol. In other words, we will sketch a picture of an equation in two variables. We will accomplish this by choosing a number for x and then finding a corresponding value for y.

Are you ready to dive into the "real world" of inequalities. Since the line itself is not a part of the solution, it is shown as a dashed line and the half-plane is shaded to show the solution set.

Solution This graph represents every real number greater than 4. Remember, adding the same quantity to both sides of an inequality does not change its direction. Again, compare the coefficients of x in the two equations. Define a variable, write an inequality, and solve each problem.

Check your solution. Twice a number is more than the sum of that number and 9. 62/87,21 Let n = the number. The solution set is {n | n >9}. To check substitute three different values into the original inequality: 9.

The problem requires solving for r. Example 13 Write an algebraic statement represented by the following graph. If the same quantity is added to each side of an inequality, the results are unequal in the same order.

Example 1 If 5. 8, then 5 + 2 8 + 2. Solve each inequality. Then graph the solution set on a number line. x í 3 > 7 Define a variable, write an inequality, and solve each problem. Check your solution. Solve each inequality.

Then graph the solution y Define a variable, write an inequality. Define a variable, write an inequality, and solve each problem. Check your solution. Three fourths of a number decreased by nine is at least forty-two. 62/87,21 Let n = the number.

Solve an Inequality

The solution set is {n|n 68}. To check this answer, substitute a number greater than or equal to 68 into the original. Solving Word Problems in Algebra Inequality Word Problems. Highlight the important information and key words that you need to solve the problem.

Identify your variables. Write the equation or inequality. Solve. He withdraws $25 each week for food, clothes, and movie tickets. For each country, write a linear inequality and graph it using thesanfranista.com Use the graph to decide on the number of food packages and medicine packages that each country should give.

(all countries should give the same amount each).

Write an inequality for each problem
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define a variable and write an inequality for each thesanfranista.com solve. Nineteen