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 2(2x + 3) = -6(x + 9)?

Back

The first step is to distribute the numbers outside the parentheses: 4x + 6 = -6x - 54.

Front

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

Back

To isolate the variable, first combine like terms by adding 2x to both sides and subtracting 19 from both sides, resulting in 9x = 36.

Front

What is the solution to the equation 6(2x + 1) = 18?

Back

The solution is x = 1.

Front

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

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

What is the solution to the equation 10 = 3x - 12?

Back

The solution is x = 22/3.

Front

What does it mean to have a variable on both sides of an equation?

Back

Having a variable on both sides means you need to rearrange the equation to isolate the variable, often by adding or subtracting terms from both sides.

Front

What is the solution to the equation 8x + 2 + 3x + 5 = x + 12?

Back

The solution is x = 1/2.