Related Topics:

Algebra Word Problems

Common Core (Algebra)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

### Suggested Learning Targets

Solving and explaining simple algebraic equations.

Recognize that properties of equality apply to equations containing unknown values by making connections to real numbers.

How to solve equations by using multiplicative and additive inverses?

**Solving One Step Equations: The Basic**

This video explains how to solve basic one step equations.

Examples:

Solve each equation.

1. x - 8 = 21

2. x + 4 = 11

3. 9 = x - 10

4. 17 = x + 2

5. x - 5 = -16

6. x + 4 = -17

Solve each equation.

1. 5x = 75

2. x/4 = 8

3. 2 = 6x

4. -3 = x/-3

5. 2/3 y = 16

**Solving One Step Equations By Addition and Subtraction**

This video introduces the solving basic equations by addition and subtraction using whole numbers.

Examples:

Determine whether the given values are solutions to the equations.

1. x - 18 = 33, is x = 43 a solution?

2. x + 27 = 51, is x = 24 a solution?

Solve each equation.

1. x - 8 = 15

2. y + 23 = 41

3. 43 = x + 9

4. 23 = y - 15

If after writing your check for your rent in the amount of $650, the new account balance is $437. What is the beginning balance?

**Solving One Step Equations Involving Decimals**

This video provides four examples of solving one step linear equations involving decimals.

Examples:

x - 2.17 = 9.9

x + 4.93 = 10.475

x/1.2 = 4.7

3.5x = 6.475

**Solve One Step Equations with Fractions**

This video provides several examples of how to solve one step equation containing fractions.

Examples:

x + 1/20 = 1/5

x - 2/3 = 3/4

3/4x = 15/28

6x = 4/15

-4/9 x = 14/15

**Solving One Step Equations Involving Fractions**

This video explains how to solve one step equations involving fractions.

Examples:

Solve each equation.

1. x - 1/2 = 1/4

2. x + 3/4 = 4/5

Solve each equation.

1. 2/3 x = 4/21

2. 5y = 10/13

3. -2/7 x = 4/5

**Solving One Step Equations: A Summary.**

Examples:

Solve each equation.

1. x - 8 = -12

2. -6 = y + 23

3. x + 1/2 = 7

4. -3 + z = 15

Solve each equation.

1. 5x = 75

2. -15 = -t

3. m/-4 = 11

4. 2/3 y = 16

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Algebra Word Problems

Common Core (Algebra)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

- Assuming an equation has a solution, construct a convincing argument that justifies each step in the solution process. Justifications may include the associative, commutative, and division properties, combining like terms, multiplication by 1, etc.

Solving and explaining simple algebraic equations.

Recognize that properties of equality apply to equations containing unknown values by making connections to real numbers.

How to solve equations by using multiplicative and additive inverses?

This video explains how to solve basic one step equations.

Examples:

Solve each equation.

1. x - 8 = 21

2. x + 4 = 11

3. 9 = x - 10

4. 17 = x + 2

5. x - 5 = -16

6. x + 4 = -17

Solve each equation.

1. 5x = 75

2. x/4 = 8

3. 2 = 6x

4. -3 = x/-3

5. 2/3 y = 16

This video introduces the solving basic equations by addition and subtraction using whole numbers.

Examples:

Determine whether the given values are solutions to the equations.

1. x - 18 = 33, is x = 43 a solution?

2. x + 27 = 51, is x = 24 a solution?

Solve each equation.

1. x - 8 = 15

2. y + 23 = 41

3. 43 = x + 9

4. 23 = y - 15

If after writing your check for your rent in the amount of $650, the new account balance is $437. What is the beginning balance?

This video provides four examples of solving one step linear equations involving decimals.

Examples:

x - 2.17 = 9.9

x + 4.93 = 10.475

x/1.2 = 4.7

3.5x = 6.475

This video provides several examples of how to solve one step equation containing fractions.

Examples:

x + 1/20 = 1/5

x - 2/3 = 3/4

3/4x = 15/28

6x = 4/15

-4/9 x = 14/15

This video explains how to solve one step equations involving fractions.

Examples:

Solve each equation.

1. x - 1/2 = 1/4

2. x + 3/4 = 4/5

Solve each equation.

1. 2/3 x = 4/21

2. 5y = 10/13

3. -2/7 x = 4/5

Examples:

Solve each equation.

1. x - 8 = -12

2. -6 = y + 23

3. x + 1/2 = 7

4. -3 + z = 15

Solve each equation.

1. 5x = 75

2. -15 = -t

3. m/-4 = 11

4. 2/3 y = 16

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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