algebraic expressions

6 times the quantity 17b minus 19 the quantity 17b minus 19 17b - 19 6 times the quantity 17b minus 19 6(17b - 19)

4 times the sum of 3 plus x squared x squared means we raise x to the power of 2: x^2 3 plus x squared: 3 + x^2 4 times the sum of 3 plus x squared 3(3 + x^2)

8 times 4 plus m squared m squared means we raise m to the power of 2 m^2 4 plus m squared: 4 + m^2 8 times 4 plus m squared 8(4 + m^2)

sum of the cube of x and half of y The cube of x means we raise x to the 3rd power: x^3 half of y means we divide y by 2: y/2 sum of the cube of x and half of y means we add y/2 to x^3 x^3 + y/2

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. Solve for x. Let's build this algebraic expression in pieces: The phrase differs from means a difference. x - 3 By less than 2/7 means we use the < sign compared to 2/7 x - 3 < 2/7 Finally...

The opposite of the difference of h and 5 The difference of h and 5 h - 5 The opposite of the difference of h and 5 means we multiply the difference of h and 5 by -1: -(h - 5) Distribute the negative sign: 5 - h

The sum of 2x and y is at least 20 The sum of 2x and y: 2x + y The phrase is at least means an inequality. We write this as >= or greater than or equal to: 2x + y >= 20

a more than b is greater than 6 a more than b: b + a Is greater than 6 means an inequality using the > sign: b + a > 6

A is thrice as much as B Thrice means multiply by 3, so we have A = 3B

The sum of the product and quotient of the numbers x and y the product of the numbers x and y xy The quotient of the numbers x and y x/y The sum of the product and quotient of the numbers x and y xy + x/y

half of c subtracted from the sum of a and b The sum of a and b: a + b half of c means we divide c by 2: c/2 half of c subtracted from the sum of a and b: a + b - c/2

1/3 of the sum of a number and 2 plus 5 is -20 The phrase a number means an arbitrary variable, let's call it x. x the sum of a number and 2: x + 2 1/3 of the sum of a number and 2 1/3(x + 2) 1/3 of the sum of a number and 2 plus 5 1/3(x + 2) + 5 The phrase is means equal to, so we set...

If n% of 400 is 260, then what is 20% of n? n% = n/100, so we have: n/100 * 400 = 260 400n/100 = 260 4n = 260 Using our equation calculator, we type this in our math engine and we get: n = 65 20% of 65 = 13

67 less than the quantity 96 times q 96 times q: 96q 67 less than the quantity 96 times q 96q - 67

Multiply 3w by the sum of v and 2u the sum of v and 2u: v + 2u Multiply 3w by the sum of v and 2u 3w(v + 2u)

Multiply t by 4 then multiply s by the result Multiply t by 4 4t Then multiply s by the result 4st

y is the sum of twice a number and 3 The phrase a number means an arbitrary variable, let's call it x. x twice a number means we multiply x by 2: 2x the sum of twice a number and 3: 2x + 3 The word is means equal to, so we set 2x + 3 equal to y y = 2x + 3

Cube the difference of b and c the difference of b and c: b - c Cubing means raising to the power of 3: (b - c)^3

-p multiplied by 15 -15p

2 is added to 3/5 of d 3/5 of d: 3d/5 2 is added to 3/5 of d 3d/5 + 2