when you have to add or subtract from each side of a linear equations and linear inequalities, how do I know what to add or subtract?
5x + 10 = 20
We need to SUBTRACT 10 from both sides.
5x +10 - 10 = 20 - 10
5x = 10
3x - 8 = 7
We need to ADD 8 to both sides.
3x - 8 + 8 = 7 + 8
3x = 15
In other words we need to get the unknown quantity by itself.
Okay thank you.
You're welcome.
When you need to add or subtract from each side of a linear equation or linear inequality, you should aim to isolate the variable on one side of the equation or inequality sign. To determine what to add or subtract, follow these steps:
1. Identify the terms involving the variable on both sides of the equation or inequality.
2. Choose the side that has the smaller coefficient or fewer terms, if possible. This will make the process easier.
3. Determine the operation needed to move all the terms involving the variable to the chosen side.
Here are some scenarios to help clarify the steps:
Scenario 1: Linear Equation
Suppose you have the equation: 3x + 5 = 7x - 3.
To isolate the variable on one side, you need to move the terms with x to one side. In this case, we'll subtract 7x from both sides to eliminate the x terms on the right side of the equation: (3x + 5) - 7x = (7x - 3) - 7x.
Simplifying: 3x - 7x + 5 = 7x - 7x - 3.
Combine like terms: -4x + 5 = -3.
Now you can continue solving for x.
Scenario 2: Linear Inequality
Consider the inequality: 2x + 4 < 6x - 2.
To isolate the variable, you need to move the terms with x to one side. In this case, we'll subtract 2x from both sides to eliminate the x terms on the right side of the inequality: (2x + 4) - 2x < (6x - 2) - 2x.
Simplifying: 2x - 2x + 4 < 6x - 2 - 2x.
Combine like terms: 4 < 4x - 2.
Now you can continue solving for x.
Remember, the goal is to perform the same operation on both sides of the equation or inequality to maintain balance. By following these steps, you can determine what to add or subtract to isolate the variable on one side.