One-Step Equations and Inequaties

One-Step Equations and Inequalities

​MGSE6.EE.7

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

​Learning Targets

1. I can write equations and solve one-step equations involving positive numbers to represent realworld problems.

2. I can write and solve one-step equations with nonnegative rational numbers from real-world problems.

3. I can solve and write equations for real-world mathematical problems containing one unknown.

​Vocabulary Words

Algebraic Expression

Equation

Inequatlity

Numeric Expression

Operation

Variable

​Essential Questions

How can variables be used to represent and solve equations and inequalities in real world problems?

How can an equation be used to represent and solve a real world/mathematical situation?

How can you use inverse operations in solving one-variable equations?

How can an inequality be used to represent and solve a real world/mathematical situation?

​Expressions vs. Equations

​Solving Equations

​GOAL: isolate the variable (get the variable by itself)

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​STEPS TO SOLVE:

​1. Use inverse operations 

• Addition and subtraction

• Multiplication and division 

2. Whatever operation you do to one side, you must do to the other side

3. Check your answer by plugging the x-value back in to the original equation

Multiple Select

What are the two basic rules for solving algebraic equations?

• Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

• Negative signs can be ignored

• Always start on the left side, regardless of where the variable is

• Always use inverse operations

Multiple Choice

What is one difference between an algebraic expression and an equation?

• Algebraic expressions do not have variables, but equations do have variables

• Expressions and equations are not different

• Expressions do not have an equal sign and equations need to have an equal sign

• Expressions need to have an equal sign and equations do not have an equal sign

Multiple Choice

Solve:

2x = 16

• -8

• $$\frac{1}{8}$$

• 8

• $$\frac{-1}{8}$$

Multiple Choice

Solve:

y + 9 = 10

• 1

• -1

• 19

• -19

​Writing Expressions and Equations from Word Problems

​*Look for clue words that help you determine which operation should be used.

​*Phrases such as, "equals", "is", and "is equal to" indicate an equation rather than an expression

Multiple Choice

twice a number plus 8

• 2 + 8a

• 8 - 2a

• 2a + 8

• $$\frac{a}{2}$$ + 8

Inequality Review

Solving Inequalities

Just like equations, except there's a different symbol in the middle!

1. Distribute
2. Combine Like Terms
3. Move the Smaller x
4. Add/subtract
5. Multiply/divide

One & Two Step Inequalities

Let's practice!

1. Add/Subtract
2. Mutliply/Divide

Inequality Symbols

Multiple Choice

Which symbol means greater than or equal to?

• $$<$$

• $$>$$

• $$\ge$$

• $$\le$$

Inequalities for Comparisons

Comparing Numbers & Expressions

Plotting & Reading Inequalities

On a number line.

Multiple Choice

What does a closed point and a ray pointing left tell you about an inequality?

• It is less than or equal to the point.

• It is greater than or equal to the point.

• It is less than the point.

• It is greater than the point.

Real-Life Inequalities

Inequality Key Words

Multiple Choice

Which sign should be used when a math phrase states that it has a maximum?

• Less than.

• Less than or equal to.

• Greater than.

• Greater than or equal to.

​Solving Equations and Inequalities

​When solving an equation, you must use inverse operations to isolate the variable.

​

​When solving an inequality, you must use inverse operations to isolate the variable.

Multiple Choice

Which type of symbol is used for an inequality?

• =

• +

• >

• pi

Multiple Choice

What is the meaning of this symbol: > ?

• Is not equal to

• is greater than

• is less than

• is equal to

Multiple Choice

What is the meaning of this symbol:  $$\le$$   ?

• is greater than or equal to

• is equal to 

• is less than or equal to 

• is less than

Multiple Choice

What is the meaning of this symbol: < ?

• is less than

• is greater than or equal to

• is equal to

• is less than or equal to

Multiple Choice

What is the meaning of this symbol:  $$\ge$$  ?

• is less than

• is less than or equal to

• is greater than 

• is greater than or equal to

​Solution v. Solution Set

​An equation will usually yield only one solution like the equation that is solved on the right.

​

​Solution

​a means of solving a problem.

​Solution V. Solution Set

​An inequality will usually yield more than one solution. This is due to meaning of the inequality symbols, and it is this reason why the solutions set must be graphed.

​

​Solution Set

​

​a complete set of numbers that satisfy(make true) an equation or inequality.

​Inequalities and NegativeNumbers

​

​When multiplying or dividing a negative number on both sides of the inequality,

​

​You must reverse the symbol in order for the inequality to remain true.

​Notice in the inequality, when -6 is divided on both sides.

Multiple Choice

An inequality solved using...

• a ruler

• a compass

• same operations

• inverse operations

Multiple Choice

When multiplying or dividing a negative number, you must...

• keep the same inequality symbol

• change the inequality to an equal sign

• reverse the inequality symbol

​Graphing Inequalities

​Since inequalities will usually yield more than one solution, it is important to see the possible solutions visually using a number line.

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​Graphing Inequalities

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Multiple Choice

$$<,\ >$$  

What type of circle must you have for these inequality symbols?

• Open circle

• small circle

• closed circle 

• large circle

Multiple Choice

What type of circle must you have for these inequality symbols?

$$\le,\ \ge$$  

• Open circle

• small circle

• closed circle

• large circle

Multiple Choice

For these symbols, what direction do you shade the number line?

$$<,\ \le$$  

• shade up

• shade right

• shade down

• shade left

Multiple Choice

For these symbols, what direction do you shade the number line?

$$>,\ \ge$$  

• shade up

• shade right

• shade left

• shade down