Creating Algebraic Expressions
Write an algebraic expression for: “5 more than a number x.”
x + 5
*NOTE: variable can be any letter (not just 'x')
Evaluate the expression 3x+4 when x = 2
= 3(2)+ 4
= 6+4
= 10
Write an equation for: “The sum of a number and 5 is 12.”
x + 5 = 12
x + 4 = 10
solve for x
x = 6
Define what an independent variable and a dependent variable is
Independent Variable: The variable that will change
Dependent Variable: The variable that will not change
Write an algebraic expression for: “The product of 3 and a number, decreased by 7.”
3y−7
*NOTE: can use any variable
Evaluate the expression 5y−3 when y=4
= 5(4)−3
=20−3
=17
Write an equation for: “Three times a number is equal to 18.”
3y=18
4y - 3y + 4 = 12
Solve for y
4y - 3y = 1y or y. So,
4y - 3y + 4 = 12
y + 4 = 12
y + 4 - 4 = 12 - 4
y = 8
Write an algebraic expression that includes the following labelled components
1) variable
2) coefficient
3) constant
e.g.
3y + 4
3 = coefficient
y = variable4 = constant
Write an algebraic expression for: “The quotient of a number and 4, increased by 2.”
m/4 + 2
*Note: can use any variable
Evaluate the expression 2a+3b−c when a=3, b=2 and c=5
= 2(3) + 3(2)−5
=6 + 6 − 5
=12 - 5
= 7
Write an equation for: “Twice the sum of a number and 4 equals 16.”
2(p+4)=16
7x + 2 −3x =18
Solve for x
7x + 2 −3x =18
7x - 3x + 2 = 18
4x + 2 = 18
4x + 2 - 2 = 18 - 2
4x = 16
4x / 4 = 16 / 4x = 4
Explain the difference between an algebraic expression and an equation. Provide examples for each.
An algebraic expression is a combination of numbers, variables, and operations (like addition, subtraction, multiplication, or division). It does NOT have an equal sign (=). It represents a value, but we don’t know the exact value until we substitute numbers for the variables.
Ex. 4y + 10
An equation is a statement that shows two expressions are equal. It always has an equal sign (=) in the middle. An equation says that one side of the equation has the same value as the other side.
Ex. 4y + 10 = 9
Translate this into an algebraic expression: “Three times the sum of a number and 2, divided by 5.”
[ 3 (n + 2)] / 5
*Note: can use any variable
Evaluate 6x2 + 4y when x=2 and y=3
6(2)2+4(3)
=6(4)+12
=24+12
=36
Write an equation for: “The square of a number, decreased by 3, equals 19.”
z2 - 3 = 19
6b + 4 −2b + 3a =14
a = 3. Solve for b
6b + 4 −2b + 3a =14
6b - 2b + 4 + 3a = 14
4b + 4 + 3(2) = 144b + 4 + 6 = 14
4b + 10 = 144b + 10 - 10 = 14 - 10
4b = 4
4b / 4 = 4/4
b = 1
Mrs.Negative Seven is trying to figure out how much money she has saved. She starts with $30 in her wallet and adds $10 each week from her part-time job. After 5 weeks, she realizes that she has $80 in total. Write an equation and find out how many weeks it took her to save that amount.
30+10w=80
10w + 30 - 30 = 80 - 30
10w = 50
10w / 10 = 50 /10
w = 5
Therefore it took Mrs. Negative 7, 5 weeks to save 80$
Translate this into an algebraic expression: “The sum of the squares of a number and 3, decreased by 2.
x2 + 32 - 2
*Note: can use any variable
Evaluate 2x2 − 3y + 5z + 4 when x=2, y=3, and z=6
= 2(2)2 − 3y + 5z + 4
= 2(4) - 3(3) + 5(6) + 4
= 8 - 9 + 30 + 4
= -1 + 30 + 4
= 29 + 4
= 33
Write an equation for: “The product of 2 less than a number and 3 is equal to 5 more than the number.”
3(p−2)=p+5
4a + 4b + 5c - 4b = 20
Solve for a, when b = 1, c = 2.
2a + 4b + 5c - 4b = 20
2a + 4b - 4b + 5c = 20
2a + 4(1) - 4(1) + 5(2) = 20
2a + 4 - 4 + 10 = 20
2a + 0 + 10 = 20
2a + 10 = 20
2a + 10 - 10 = 20 - 10
2a/2 = 10/2
a = 5
Mrs. Brace is buying tickets for herself and her family to go to a concert by Emily Wonder. The cost of each ticket is $9. She also has to pay a one time $6 service fee and wants to spend no more than $60 in total for the tickets. How many tickets can Mrs. Brace buy for no more than $60?
9t + 6 = 60
9t + 6 - 6 = 60 - 6
9t = 54
9t / 9 = 54 / 9
t = 6
Therefore, Mrs. Brace can buy 6 tickets with 60$.