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 6(2x + 1) = 18?

Back

Distribute the 6 to both terms inside the parentheses: 12x + 6 = 18.

Front

How do you isolate the variable in the equation 7 - 5x = 12?

Back

Subtract 7 from both sides to get -5x = 5, then divide by -5 to find x = -1.

Front

What is the solution to the equation 2 - 4x = 3x - 12?

Back

The solution is x = 2.

Front

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

Back

First, distribute -2: 7 - 20x - 2 = 25. Then combine like terms and isolate x to find x = -1.

Front

How do you solve for x in the equation 10 = 3x - 12?

Back

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

Front

What is the importance of checking your solution in a linear equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when the variable cannot be isolated, often resulting in a false statement (e.g., 0 = 5).

Front

What does it mean for an equation to have infinitely many solutions?

Back

An equation has infinitely many solutions when any value of the variable satisfies the equation, often resulting in a true statement (e.g., 0 = 0).