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 7x + 5 + x - 3 + x = 5?

Back

Combine like terms on the left side: 7x + x + x + 5 - 3 = 5, which simplifies to 9x + 2 = 5.

Front

How do you isolate the variable in the equation 10 = 3x - 12?

Back

Add 12 to both sides to get 22 = 3x, then divide both sides by 3 to find x = 22/3.

Front

What is the solution to the equation 7 - 2(10x + 1) = 25?

Back

First, distribute -2: 7 - 20x - 2 = 25. Then combine like terms: 5 - 20x = 25. Subtract 5 from both sides: -20x = 20, so x = -1.

Front

What does it mean to combine like terms?

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 5 + 3x = 8x - 15?

Back

First, rearrange the equation: 3x - 8x = -15 - 5. This simplifies to -5x = -20, so x = 4.

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 7 - 5x = 12?

Back

Subtract 7 from both sides: -5x = 5. Then divide by -5 to find x = -1.

Front

What is the importance of the equal sign in a linear equation?

Back

The equal sign indicates that the expressions on both sides of the equation are equivalent.