algebraic expressions

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase a number means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number...

a is multiplied by 2 and added to b a is multiplied by 2: 2a Added to be: 2a + b

the square of the sum of x and y is less than 20 The sum of x and y means we add y to x: x + y the square of the sum of x and y means we raise the term x + y to the 2nd power: (x + y)^2 The phrase is less than means an inequality, so we write this as follows: (x + y)^2 < 20

17 decreased by three times d equals c three times d means we multiply d by 3: 3d 17 decreased by three times d means we subtract 3d from 17 17 - 3d The word equals means an equation, so we set 17 - 3d equal to c: 17 - 3d = c

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: The phrase at least means greater than or equal to...

product of r plus 7 and 4 r plus 7 means we add 7 to r: r + 7 The product means we multiply the expression r + a 7 by 4: 4(r + 7)

raise r to the 8th power then find the product of the result and 3 Raise r to the 8th power means we raise r with an exponent of 8: r^8 The product of the result and 3 means we muliply r^8 by 3 3r^8

The sum of a and b added with the quotient of x and y. The sum of a and b is written as: a + b The quotient of x and y is written as: x/y The phrase added with means we add x/y to a + b: a + b + x/y

5 times the sum of 3 times a number and -5 The phrase a number means an arbitrary variable, let's call it x: x 3 times a number means we multiply x by 3: 3x the sum of 3 times a number and -5 means we add -5 to 3x: 3x - 5 5 times the sum means we multiply 3x - 5 by 5: 5(3x - 5)

9 less than twice x is twice y Twice x means we multiply x by 2: 2x 9 less than Twice x means we subtract 9 from 2x 2x - 9 Twice y means we multiply y by 2: 2y The word is means equal to, so we set 2x - 9 equal to 2y: 2x - 9 = 2y

The difference of 25 and a number added to triple another number The phrase a number means an arbitrary variable, let's call it x: x The difference of 25 and a number means we subtract x from 25: 25 - x The phrase another number means a different arbitrary variable, let's call it y: y Triple...

r squared plus the product of 3 and s plus 5 r squared means we raise r to the power of 2 r^2 The product of 3 and s means we multiply s by 3: 3s plus 5 means we add 3s + 5 R squared plus means we add r^2: r^2 + 3s + 5

two thirds of a number is no more than -10 The phrase a number means an arbitrary variable, let's call it x: x Two thirds of a number mean we multiply x by 2/3: 2x/3 The phrase no more than -10 means less than or equal to -10, so we have an inequality: 2x/3 <= -10

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time? Total weight = average weight per person * Number of people Total weight = 150p We know from the problem that...

Add 5 to the sum of 2x and y The sum of 2x and y means we add y to 2x: 2x + y Add 5 2x + y + 5

The quotient of t and 12 is the sum of s and r. Step 1: The quotient of t and 12 is: t/12 Step 2: The Sum of s and r is s + r Step 3: The word is means equal to, so we set t/12 equal to s + r t/12 = s + r

twice the product of p q and r The product of p q and r means we multiply all 3 variables together: pqr The word twice means we multiply pqr by 2: 2pqr

twice the square root of a number increased by 5 is 23 The phrase a number means an arbitrary variable, let's call it x: x The square root of a number means we raise x to the 1/2 power: sqrt(x) the square root of a number increased by 5 means we add 5 to sqrt(x): sqrt(x) + 5 twice the square...

cube root of a number and 7 The phrase a number means an arbitrary variable, let's call it x: x Cube root of a number means we raise x to the 1/3 power: x^1/3 And 7 means we add 7: x^1/3 + 7

The sum of x and 10 equals the sum of 2 times x and 12 The sum of x and 10 means we add 10 to x: x + 10 2 times x means we multiply x by 2: 2x the sum of 2 times x and 12 means we add 12 to 2x: 2x + 12 The sum of x and 10 equals the sum of 2 times x and 12: x + 10 + (2x + 12) Distribute the...