How do you distribute an equation
In order to distribute an equation, you need to perform multiplication or division on both sides of the equation to ensure that each term is distributed based on the operations being performed.
Here are the steps to distribute an equation:
1. Identify the equation: Start with an equation that contains terms on both sides, often separated by an equal sign (=).
2. Determine the operation: Determine which operation (multiplication or division) needs to be distributed to each term. This could be based on the specific equation or the desired transformation.
3. Apply the operation to both sides: Perform the same operation on both sides of the equation to distribute it. Make sure to perform the operation on each term individually.
4. Simplify both sides (if needed): After distributing the equation, simplify both sides by combining like terms, rearranging the terms, or performing any necessary calculations.
5. Check the solution: If solving for a variable, check your solution by substituting it back into the original equation to verify its correctness.
Here's a simple example to illustrate the process:
Original equation: 2(x + 3) = 10
Step 1: Identify the equation: 2(x + 3) = 10
Step 2: Determine the operation: We need to distribute the multiplication operation to the terms inside the parentheses.
Step 3: Apply the operation to both sides: Multiply each term inside the parentheses by 2.
2(x + 3) = 10
2 * x + 2 * 3 = 10
2x + 6 = 10
Step 4: Simplify both sides (if needed): Combine like terms on the left side.
2x + 6 = 10
Step 5: Check the solution: Substitute the value of x back into the original equation.
2(x + 3) = 10
2(4 + 3) = 10
2(7) = 10
14 = 10
Since the resulting equation is false, the solution is incorrect. This means there may be an error in the distribution or a mistake in the solution process.
To distribute an equation, you follow the process known as the distributive property. This property allows you to distribute a factor to all the terms inside parentheses. Here's a step-by-step guide:
Step 1: Identify the expression that needs to be distributed. This expression will usually be inside parentheses.
Step 2: Multiply the term outside the parentheses by each term inside the parentheses. This means you will have to perform multiplication for each term inside the parentheses.
Step 3: Simplify the equation by combining like terms, if necessary.
Let's look at an example to illustrate the process:
Example: Distribute the expression 3(x + 2) - 4(2x - 1)
Step 1: Identify the expressions to be distributed: (x + 2) and (2x - 1)
Step 2: Distribute the 3 and 4 to each term inside the parentheses:
3(x) + 3(2) - 4(2x) + 4(-1)
Step 3: Simplify the equation by combining like terms, if any:
3x + 6 - 8x - 4
Now you have the distributed equation: 3x - 8x + 6 - 4
Remember to simplify the equation further if possible.