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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation1.14 Basic Operations With Variables - II

 Algebraic Notation: Verbal phrases may be translated into algebraic expressions. Examples: The product of a and b = a . b = ab = a x b The sum of a and 4 = a + 4 x decreased by 9 = x - 9 y divided by 3 = y/3 A number increased by 6 = n + 6 Two times a number and that product decreased by 5 = 2x - 5 A number divided by 3 and that quotient increased by 2 = n/3 + 2 Twice the sum of x and 4 = 2(x + 4) Example: Write an algebraic expression for "a number times itself plus another number added to itself." Solution: Let the number be 'x'. The number times itself is x2. Let another number be 'y'. The second number added to itself is 2y. Therefore, a number times itself plus another number added to itself is x2+2y. Example: Write an algebraic expression for "quotient of a number times ten and the same number increased by 4." Solution: Let the number be 'x'. Then number times ten is 10x. The same number increased by 4 is x + 4. Therefore, quotient of a number times ten and the same number increased by 4 is = 10x / (x+4) Directions: If x is a non-zero number, express the following in terms of x. Also write at least 10 examples of your own.
 Q 1: 5 more than twice x.2+5X2x+5(5+2)x5+x2 Q 2: 3 times x.xxx3x3+3+33+x Q 3: Three consecutive integers beginning with x and greater than x.x, x-1 and x-2x, x+1 and x+2x, 2x, 3x1, 2, and 3 Q 4: 6 more than a number.6xx - 6x/6x + 6 Q 5: Sum of squares of x and 4.x+4x2+162x+2*4 Q 6: A number divided by 9.r/9r + 99/r9r Q 7: The product of a number and 8.a/88anxn+8a + 8 Q 8: 4 less than half of x.4-2/x4/2-x4-X/2x/2-4 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!