Unit 6: Expressions & Equations
LESSON 2: ALGEBRAIC EXPRESSIONS & EQUATIONS
APRIL 20, 2021
We have been talking all about expressions, which are mathematical sentences including numbers, variables and operations.
Today, we will be talking about how we can combine expressions to form equations and inequalities!
WHAT IS AN EQUATION?
An EQUATION is a mathematical sentence that states that two expressions are EQUAL.
*Think: EQUATIONS are EQUAL.
Ex. 3 + 4 = 7 is an equation because the expressions β3 + 4β and β7β are equal.
WHAT IS AN INEQUALITY?
An INEQUALITY is a mathematical sentence that states that two expressions are NOT EQUAL.
*Think: INEQUALities are UNEQUAL.
Ex. 3 - 2 < 7 is an inequality because the expressions β3 - 2β and β7β are unequal. 3 - 2 is less than 7.
Do you remember your inequality signs?
Drag the red star to the GREATER THAN sign.
Drag the yellow star to the NOT EQUAL sign.
Drag the blue star to the LESS THAN sign.
> < β
How did you do? Remember to add your crocodile teeth if you need to! (Mine are a little wavy.)
> < β
10 1
GREATER THAN
4 18
NOT EQUAL
9 52
LESS THAN
Drag the inequality symbols into the blanks to make the following statements true.
14 ________ 25
320 ________ 319
The next few questions will ask for you to write an inequality or equation to describe the expressions given.
EXAMPLE:
Expressions:
A number plus seven is greater than 2.
*Remember, βa numberβ we donβt know is going to be a variable!
Inequality:
x + 7 > 2
*You can pick ANY letter - it doesnβt have to be x!
You try! Write an equation based on the expression.
Expressions:
A number minus 9 is equal to 4.
*Remember, βa numberβ we donβt know is going to be a variable!
Equation:
ANSWER:
Expressions:
A number minus 9 is equal to 4.
*Remember, βa numberβ we donβt know is going to be a variable!
Equation:
y - 9 = 4
Write an inequality to describe the expressions.
Expressions:
Four times a number is less than the same number plus 9.
*Remember, βa numberβ we donβt know is going to be a variable!
Inequality:
ANSWER:
Expressions:
Four times a number is less than the same number plus 9.
*Remember, βa numberβ we donβt know is going to be a variable!
Equation:
4g < g + 9
Write an equation to describe the expressions.
Expressions:
A number divided by 10 is equal to 2 more than 95.
*Remember, βa numberβ we donβt know is going to be a variable!
Equation:
ANSWER:
Expressions:
A number divided by 10 is equal to 2 more than 95.
*Remember, βa numberβ we donβt know is going to be a variable!
Equation:
s / 10 = 95 + 2
One more vocabulary word!
A solution to an equation or inequality is any value that makes the mathematical statement true!
Example: When x + 4 = 5, the solution is that x = 1!
Example: When 8 - y > 3, one possible solution is y = 4!
IS 2 THE SOLUTION THE EQUATION BELOW?
8d + 5 = 21
Circle your answer:
YES
NO
Show your work to explain why:
IS 6 THE SOLUTION THE EQUATION BELOW?
2d - 4 = 9
Circle your answer:
YES
NO
Show your work to explain why:
IS THIS INEQUALITY TRUE OR FALSE?
80a + 11 < 121 when a = 2
Circle your answer:
TRUE
FALSE
Show your work to explain why:
IS 14 A SOLUTION TO THIS INEQUALITY?
y - 6 < 30
Circle your answer:
YES
NO
Show your work to explain why:
Look at all of the new words weβve learned this week! Building your math vocabulary gives you tools you can use to explain your strategies.
expression solution
evaluate variable
equation inequality