Solving Linear Equations and Operations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you solve the equation 5x - 4 + 2x = 3?

Back

Combine like terms: 7x - 4 = 3. Then add 4 to both sides: 7x = 7. Finally, divide by 7: x = 1.

Front

What is the opposite operation of addition?

Back

Subtraction.

Front

What is the opposite operation of multiplication?

Back

Division.

Front

What does it mean to isolate a variable in an equation?

Back

To isolate a variable means to manipulate the equation so that the variable is on one side of the equation by itself.

Front

How do you solve the equation -15 = 5a + 12 - 2a + 6?

Back

Combine like terms: -15 = 3a + 18. Subtract 18 from both sides: -33 = 3a. Divide by 3: a = -11.

Front

What is the solution to the equation 4(a + 3) = -32?

Back

First, divide both sides by 4: a + 3 = -8. Then subtract 3 from both sides: a = -11.

Front

How do you solve the equation 2x - 3 + 4x = 27?

Back

Combine like terms: 6x - 3 = 27. Add 3 to both sides: 6x = 30. Divide by 6: x = 5.

Front

What are inverse operations?

Back

Inverse operations are pairs of operations that undo each other, such as addition and subtraction or multiplication and division.

Front

What is the purpose of using inverse operations when solving equations?

Back

The purpose is to 'undo' operations applied to the variable, allowing you to isolate it and find its value.