Testing and Writing Equations and Inequalities

Testing and Writing Equations and Inequalities

In this lesson we will cover Standards 6.EE.B.5 and 6.EE.B.6. You will learn how to use substitution to determine if a number is a solution to an equation or inequality and how to use variables to represent real-world situations. You will also learn to carefully consider what kind of numbers make sensible input values in real-world algebraic expressions.

Open Ended

Hello there everyone! I hope everyone is doing good this morning! Today we will be learning: Testing & Writing Equations & Inequalities, anyway, let's get started!

When Are Equations “True”?

Equations lie sometimes. In fact, it’s pretty easy

to see that the numerical equation 5 = 3 + 4 is lying right to our faces! The sooner you learn this the better: just because an equation has an equals sign, don’t trust that it’s telling the truth. Since this is a math book and not a courtroom, we don’t say that 5 = 3 + 4 is a liar; but we do say that 5 = 3 + 4 is not a valid equation, or that it is false. Conversely, we say that an equation like 5 = 3 + 2 is valid, or true.

Examples

• The equation 10 = 4 + 6 is true.

• The equation 52 = 10 is false.

• The equation 5,999,999 × 0 = 0 × (–485) is valid.

• The equation –(4) 2 = 16 is invalid.

Testing Equations

An algebraic equation is an equation that has one or more variables. (Algebraic expressions don’t have an equals sign, algebraic equations do.) Algebraic equations can be pretty sly in their deception and it takes a little more work to see if they are valid or invalid. We’ll start with a simple equation, x + 3 = 4. Whether this is a true or false equation depends on the value of x. The equation is true when x = 1, but it is false when x equals all other values.

Testing An Equation

In order to test if an equation is true for a given value, plug that value in for the variable, follow the correct order of operations to evaluate the

numerical expressions on each side of the equals sign, and see if the resulting numerical statement is true or false. Let’s try some:

Example: Is 2x = 16 true for x = 8?

Solution: 2x = 16 is true for x = 8 since 2(8) = 16.

When Are Inequalities “True”?

This varying degree of preciseness is found between equations and inequalities as well. The equation t = 10 represents meet me at my house at 10:00 A . M . , while the inequality t > 10 represents come by my house sometime after 10 A . M . Notice that the equation t = 10 has only one value for t that makes it true: 10. Meanwhile, the inequality, t > 10, has lots of potential solutions that would make it true: t = 10.5, t = 10.75, and t = 12

ERROR ALERT!

Students forget that inequalities shouldn’t always be read left to write. Reading –5 > x as negative 5 is greater than x sounds so

confusing! Instead, begin with the variable and say “is less than” if the symbol is pointing toward the variable and say “is greater than” if the symbol is pointing away from the variable. If the symbol is underlined, think of that as half of an equals sign and include “or equal to” in your translation of it:

n 7 < m: m is greater than seven

n v

n k < 42: k is less than 42

n 10

12: v is greater than or equal to 12

a: a is less than or equal to 10

Fill in the Blank

Is the equation 9 – 3² = 0 true?

Multiple Select

Is the equation c ² + 4 = 12 true for c = 4?

• yes

• no

• true

• false

• ask Sailor Mercury

Multiple Choice

On a Spanish test, the spelling questions are worth 5 points, the vocabulary questions are worth 8 points, and the verb conjugation questions are worth 10 points. If Miss Madeleine does not give any partial credit, what expression will she use to calculate the total point score for her students who get s spelling questions, v vocabulary questions, and c verb conjugations correct? What kinds of numbers make sense for each of these variables?

• s, v, and c must be a decimal below or equal to 0

• s, v, and c must be whole numbers greater than or equal to zero.

• s, v, and c must be a negative number below o

Poll

Did you enjoy this lesson?

• Yes! I learned something!

• No, I didn't learn anything either...

• Yes! But, I didn't learn anything.....

• NO! But I did learn something!

Open Ended

Well everyone, that's it! I hoped you enjoyed this lesson! Next week Monday our topic will be: Solving

One-Step Equations, until then, enjoy your weekend!😚