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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: 4 less than half of x.4/2-x4-X/2x/2-44-2/x Q 2: The product of a number and 8.a + 8nxn+88aa/8 Q 3: 3 times x.3+x3+3+33xxxx Q 4: A number divided by 9.9rr + 99/rr/9 Q 5: 6 more than a number.6xx/6x + 6x - 6 Q 6: Of the four consecutive integers x is the largest. Write the other three.x-2, x-1, xx-3, x-2, x-1x+1, x+2, x+3x-4, x-3, x-2 Q 7: 5 more than twice x.(5+2)x2+5X2x+55+x2 Q 8: Three consecutive integers beginning with x and greater than x.x, x+1 and x+2x, x-1 and x-21, 2, and 3x, 2x, 3x Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!