Mathematics Knowledge Asvab

12 less the sum of 3 and some number

12 - (3 + x)

the product of some number and 12

12x

Solve 16 + z = 24

16 + z = 24 (subtract 16 from both sides) z = 8

Evaluate 2x² + 4y + 5, if x = 2 and y = 3

2 (2)² + 4 (3) + 5 2 (4) + 12 + 5 8 + 12 + 5 = 25

Solve 2/3 a - 5 = 9

2/3 a - 5 = 9 (add 5 to both sides) 2/3 a = 14 (multiply the inverse of 2/3 to both sides) 2/3 (3/2) a = 14/1 (3/2) (divide out common factors of 14 and 2) a = 7/1 (3/1) (cross multiply) a = 21

Solve 3x + 5 > 8

3x + 5 > 8 (subtract 5 from both sides) 3x > 3 (divide 3 from both sides) x > 1

Solve 3x = 18

3x = 18 (divide both sides by 3 to isolate the variable x) 3x/3 = 18/3 x = 6

the product of 5 and the sum of x and y

5 ( x + y)

Solve 5 - 2x > 9

5 - 2x > 9 (subtract 5 from both sides) -2x > 4 (divide -2 a negative number to both sides, change sign) x > 2

the ratio of 6 and some number

6 / x

some number times 6

6x

Solve 7y = 3y - 12

7y = 3y - 12 (subtract 3y from both sides to isolate the variable) 7y - 3y = 3y - 3y - 12 4y = - 12 (divide 4 from both sides to isolate the variable) y = -12/4 (odd number of negative sign = negative answer) y = -3

some number subtracted from 8

8 - x

9 times some number plus the sum of 5 and y

9x + (5 + y)

Evaluate a + b + c, if a = 2, b = 4, and c = 3

a + b + c 2 + 4 + 3 = 9

Evaluate the fraction a + b over 4 + a over b + c, if a = 2 b=6 and c=10

a + b/4 + a/b + c 2 + 6/4 + 2/6 + 10 8/4 + 2/16 (simplify the first fraction) 2 + 2/16 (simplify the second fraction) 2 + 1/8 = 2 1/8

Equation

a mathematical statement that contains an equal ( = ) sign

How do you solve an equation for the unknown

keeping the equation balanced by doing the same operation of numbers on both sides to isolate variables on one side when adding or subtracting from one side cancel it out on that side then move the number to the other side of the equation and change its sign. multiplying or dividing by the same number on both sides works the same way

Variable

letter that represents a number and can change in value

Multiplying or Dividing Negative numbers when solving fo rinequalities

reverse the sign of the number being multiplied or divided

Inequalities

statements that show certain relationships between selected variables and numbers are not equal ( ≠ ), greater than ( > ), less than ( < ), greater than or equal to ( ≥ ), and less than or equal to ( ≤ )

how do you evaluate an algebraic expression?

substitute the given value for the unknown and then perform the arithmetic operation

some number plus 7

x + 7

some number less 12

x - 12

when y is subtracted from x, the result is less than 33

x - y < 33

some number divided by 4

x / 4

some number divided by 5 or the ratio of some number and 5

x / 5

the value of x is greater than 13

x > 13

Solve x/3 = 12

x/3 = 12 (multiply 3 to both sides) x = 36

Solve x/5 - 4 = 2

x/5 - 4 = 2 (add 4 to both sides) x/5 = 6 (multiply 5 to both sides) x = 30

when x is divided by 5, the result is greater than or equal to the value of z

x/5 ≥ z

Solve y - 4 = 20

y - 4 = 20 (add 20 to both sides of the equation) y -4+4 = 20+4 y = 24

the value of y is less than 45

y < 45