algebraic expressions

n is tripled then decreased by 5 n is tripled means we multiply n by 3: 3n Decreased by 5 means we subtract 5 from 3n: 3n - 5

the sum of 4 and x split into 5 equal parts The sum of x and 4 means we add 4 to x: x + 4 Whenever you see the phrase split into, think of divide or divided by: (x + 4)/5

the midpoint between m and n The midpoint is halfway between m and n: (m + n)/2

The sum of a number and twice its reciprocal is 3 the phrase a number means an arbitrary variable, let's call it x. x The reciprocal of a number means we take 1 over that number: 1/x Twice the reciprocal means we multiply 1/x by 2: 2/x The sum of a number and twice its reciprocal x + 2/x...

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number...

A man's age (a) 10 years ago is 43. Years ago means we subtract a - 10 = 43 If the problem asks you to solve for a, we type this equation into our math engine and we get: Solve for a in the equation a - 10 = 43 Step 1: Group constants: We need to group our constants -10 and 43. To do that...

The difference between the quotient of x and y, and twice z The quotient of x and y means we divide x by y: x/y Twice z means we multiply z by 2: 2z The difference between the quotient of x and y, and twice z means we subtract 2z from x/y x/y - 2z

A farmer has c chickens. She sells 3 of them for $6 each and the rest she sells for $5 each. How much money will she receive? Total money received = 3 * 6 + 5(c - 3) Total money received = 18 + 5c - 15 Total money received = 5c + 3

X minus 5 plus x equals 79 x minus 5 x - 5 plus x x - 5 + x equals 79 x - 5 + x = 79 Group like terms: (x + x) - 5 = 79 2x - 5 = 79

66 decreased by Janelle's savings is 15 Let Janelle's savings be s. 66 decreased by s is: 66 - s The word is means equal so we set 66 - s equal to 15 66 - s = 15

triple a number and another number The phrase a number means an arbitrary variable, let's call it x: x Triple a number means we multiply x by 3: 3x The phrase another number means another arbitrary variable, let's call it y: y The word and means we add y to 3x: 3x + y

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these...

Ryan buys candy that costs $4 per pound. He will buy at least 12 pounds of candy. What are the possible amounts he will spend on candy? Clue for you: the phrase at least means an inequality. Let s be the spend on candy. Cost = Price * quantity Cost = 4 * 12 Cost = 48 The phrase at least...

q increased by the difference between 18 times q and 5 Take this algebraic expression in parts. 18 times q: 18q The difference between 18 times q and 5 means we subtract 5 from 18q: 18q - 5 q increased by the difference between 18 times q and 5 means we add 18q - 5 to q: q + (18q - 5) q +...

There are 10 more cars(c) than jeeps(j) c = j + 10

the sum of 3 numbers divided by its product The phrase 3 numbers means we choose 3 arbitrary variables. Let's call them x, y, z. The sum of of these 3 numbers is: x + y + z The phrase its product means we multiply all 3 arbitrary variables together: xyz Now, the phrase divided by means we...

3 less than a number times itself The phrase a number means an arbitrary variable, let's call it x: x Itself means the same variable as above. So we have: x * x x^2 3 less than this means we subtract 3 from x^2: x^2 - 3

triple the sum of 36 and 6 then add 4 Take this algebraic expression in parts: The sum of 36 and 6: 36 + 6 Triple the sum means we multiply the sum by 3: 3(36 + 6) Then add 4: 3(36 + 6) + 4 If the problem asks you to simplify the algebraic expression, we have: 3(42) + 4 126 + 4 130

13 is the product of 5p and 5 the product of 5p and 5 means we multiply 5p by 5: 5p * 5 25p The word is means equal to, so we set 25p equal to 13 13 = 25p 25p = 13

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2 For the phrase choose any number we can use an arbitrary variable, let's call it x. Add 2: x + 2 Multiply your answer to 3: 3(x + 2) And minus 2 which...