Solving Equations Vocabulary
A __________ is a letter or symbol that represents a number. You can choose different numbers for the value of the __________.
variable
SHOW YOUR WORK
Find the solution to this equation:
5x=25
x = 5
__________ expressions are different ways of describing the same quantity.
𝑥 + 𝑥 + 𝑥 is __________ to 3𝑥 because they both describe three copies of an unknown number, 𝑥.
equivalent
Combine like terms to generate an equivalent expression
10x+3x
13x
Evaluate 3b when b=8
24
A __________ to an equation is a value of a variable that makes the equation true. For example, 5 is a __________ to the equation 3𝑥 = 15 because 3(5) = 15.
solution
SHOW YOUR WORK
Find the solution to this equation:
x/7 = 8
x = 56
__________ describes repeated multiplication.
For example,
2^4 = 2 times 2 times 2 times 2 = 16
It is called “ to the power of ” or “ to the fourth.”
2 is called the base and 4 is called the __________
exponent
Use the distributive property to generate an equivalent expression
7(a+2)
7a+14
To __________ means to replace a variable with its given value.
substitute
A __________ is a number multiplied by a variable, usually without a symbol in between the number and the variable. In the expression 5𝑥 + 8, the __________ of 𝑥 is 5.
coefficient
SHOW YOUR WORK
Find the solution to this equation:
b+1.9 = 3.7
b = 1.8
A __________ describes two or more quantities that are being multiplied together. For example, the area of a rectangle is the __________ of 3 and 2𝑥 + 5 or 3(2𝑥 + 5).
product
Combine like terms to generate an equivalent expression
5x+10+2x+5
7x+15
What does each letter in PEMDAS stand for?
Parenthesis
Exponent
Multiplication and Division
Addition and Subtraction
A __________ is a part of an expression that involves addition. It can be a single number, a variable, or a variable and a number multiplied together. For example, the expression 5𝑥 + 8 has two __________. The first __________ is 5𝑥 and the second term is 8.
term
SHOW YOUR WORK
Find the solution to this equation:
1/2a=5/8
a = 10/8
or
a = 1 1/4
You can use the __________ __________ to perform the multiplication outside of parenthesis to the terms inside.
For example 5(x + 10) becomes 5x + 10
Distributive Property
Use the distributive property to generate an equivalent expression
0.5(8m+42)
4m+21
Evaluate 9m+11 when m=20
191
In order to solve an equation we must perform the __________ __________ on both sides to isolate the variable.
inverse operation / opposite action
Jessica purchased b books for $7.25 each. Her total was $79.75.
Write and solve an equation for how many books Jessica purchased.
7.25b=79.75
b=11
You can __________ __________ __________ if they have the same variable and exponent.
For example 3a + 2x + 5 + 4a - x -2 becomes 7a + x + 3
combine like terms
Use the distributive property to generate an equivalent expression
4y+10x+20+9y-6x-9
13y+4x+11
Evaluate when x=4
8(x+6)-7
63