One-Step Equations and Inequaties

​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?

​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

​*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

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

Let's practice!

1. Add/Subtract
2. Mutliply/Divide

Comparing Numbers & Expressions

On a number line.

Inequality Key Words

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

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

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

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​Solution

​a means of solving a problem.

​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.

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​Solution Set

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

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

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

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

​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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