Solving Linear Equations

Linear equations are equations that represent straight lines on a graph. They are in the form of y = mx + b where m is the slope and b is the y-intercept. The goal in solving linear equations is to find the value of the variable that makes the equation true.

Basic Steps for Solving Linear Equations:

1. Distribute (if necessary): If there are parentheses in the equation, use the distributive property to remove them.
2. Combine Like Terms: Combine any like terms on the same side of the equation.
3. Isolate the Variable: Use inverse operations to get the variable on one side of the equation.
4. Simplify: Perform any necessary operations to simplify the equation.
5. Check Your Answer: Substitute the solution back into the original equation to ensure it satisfies the equation.

Example:

Solve for x in the equation 2x + 5 = 15.

Step 1: Subtract 5 from both sides to isolate x.

Step 2: Divide both sides by 2 to solve for x.

Step 3: Check the solution by substituting x = 5 back into the original equation.

Practice Problems:

1. Solve for y in the equation 3y - 7 = 14.
2. Solve for a in the equation 2(a + 4) = 18.
3. Solve for m in the equation 5m - 3 = 22.

Remember, practice is key to mastering linear equations. The more you practice, the better you will become at solving them.

Good luck!

[Solving Linear Equations] Related Worksheets and Study Guides:

• Linear equationsMathematics • Eighth Grade