Notation. x y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means x is greater than y. The last two inequalities are called strict inequalities. Our focus will be on the nonstrict inequalities. Algebra of Inequalities Suppose x + 3 < 8. Addition works like for equations: x + 6 < 11 (added 3 to each side). Subtraction works like for equations: x + 2 < 7 (subtracted 4 from each side). Multiplication and division by positive numbers work like for equations: 2x + 12 < 22 =) x + 6 < 11 (each side is divided by 2 or multiplied by 1 2 ). 59 60 4. LINEAR PROGRAMMING Multiplication and division by negative numbers changes the direction of the inequality sign: 2x + 12 < 22 =) x 6 > 11 (each side is divided by -2 or multiplied by 1 2 ). Example. For 3x 4y and 24 there are 3 possibilities: 3x 4y = 24 3x 4y < 24 3x 4y > 24 4y = 3x + 24 4y < 3x + 24 4y > 3x + 24 y = 3 4x 6 y > 3 4x 6 y < 3 4x 6 The three solution sets above are disjoint (do not intersect or overlap), and their graphs fill up the plane. We are familiar with the graph of the linear equation. The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other side of the line. To determine which side for an inequality, choose a test point not on the line (such as (0, 0) if the line does not pass through the origin). Substitute this point into the linear inequality. For a true statement, the solution region is the side of the line that the test point is on; for a false statement, it is the other side.
Total: 318
Student tickets: x
Adult tickets: 3x+6
x+(3x+6)=318 -> 4x+6=318 -> 4x=312 -> x=78
3(78)+6 = 234+6 = 240
240 adult tickets were sold
Answer:
Step-by-step explanation:
Percy used to have 100% of the shirts (before he started selling them). Since then, he has given away 90% of the shirts and is now left with only 10% of what he used to have. He currently has 25 shirts, meaning that 25 is 10% of what he had.
Lets set up a proportion:
25 shirts : 10%
x shirts : 100%
x = 25*100 / 10
x = 2500 / 10
x = 250 shirts
Percy started off with 250 shirts.
Answer:
263100=2.63
Step-by-step explanation:
263100 is already in the simplest form. It can be written as 2.63 in decimal form (rounded to 6 decimal places).
