tailieunhanh - The gre anlytycal writting section 8

Tham khảo tài liệu 'the gre anlytycal writting section 8', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | -------------------------- THE GRE QUANTITATIVE SECTION ----------------------------------- Example 10 5 so 10 -3 5 -3 -30 -15 Solving Linear Inequalities To solve a linear inequality isolate the letter and solve the same as you would in a first-degree equation. Remember to reverse the direction of the inequality sign if you divide or multiply both sides of the equation by a negative number. Example If 7 - 2x 21 find x. Isolate the variable 7 - 2x 21 -7 -7 -2x 14 Because you are dividing by a negative number the inequality symbol changes direction -2x 14 -2 -2 x -7 The answer consists of all real numbers less than -7. Solving Combined or Compound Inequalities To solve an inequality that has the form c ax b d isolate the letter by performing the same operation on each member of the equation. Example If-10 -5y - 5 15 find y. Add five to each member of the inequality -10 5 -5y - 5 5 15 5 -5 -5y 20 Divide each term by -5 changing the direction of both inequality symbols ỉ 5y 5 1 y -4 The solution consists of all real numbers less than 1 and greater than -4. 175 ------------------------- THE GRE QUANTITATIVE SECTION --------------------------------- Translating Words into Numbers The most important skill needed for word problems is being able to translate words into mathematical operations. The following list will give you some common examples of English phrases and their mathematical equivalents. Increase means add. Example A number increased by five x 5. Less than means subtract. Example 10 less than a number x - 10. Times or product means multiply. Example Three times a number 3x. Times the sum means to multiply a number by a quantity. Example Five times the sum of a number and three 5 x 3 . Two variables are sometimes used together. Example A number y exceeds five times a number x by ten. y 5x 10 Inequality signs are used for at least and at most as well as less than and more than. Examples The product of x and 6 is greater than 2. x X 6 2 When 14 is added to a .