Solving Linear Equations

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

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable (usually x) that makes the equation true.

Front

What is the first step in solving the equation 3(5x + 10) + 10 = 6x - (x + 10)?

Back

Distribute the 3 on the left side: 15x + 30 + 10 = 6x - x - 10.

Front

How do you isolate the variable x in the equation 7x + 19 = -2x + 55?

Back

Combine like terms by adding 2x to both sides and subtracting 19 from both sides: 9x = 36, then divide by 9.

Front

What is the solution to the equation 2(2x + 3) = -6(x + 9)?

Back

The solution is x = -6.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the solution to the equation 2(3x + 4) + 2 = 4 + 3x?

Back

The solution is x = -2.

Front

How do you check if your solution to a linear equation is correct?

Back

Substitute the value of the variable back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

The solution is x = 2.

Front

What is the purpose of using parentheses in linear equations?

Back

Parentheses indicate that the operations inside them should be performed first according to the order of operations.