olve the equation justifying with the correct reasoning: 2(x+8)=2x +8
(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
2(x+8)=2x +8
Step 1: Response area Property to get Response area
Step 2: Response area Property to get Response area
For this equation, there is/are Response area
Properties and Reasons
Equation Steps
The option "2 x plus 8 is equal to x" (9 of 17) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
Step 1:
To solve the equation, distribute the 2 on the left side of the equation through the parentheses.
Step 2:
Simplify both sides of the equation by combining like terms.
For this equation, there is/are no extraneous solution(s).
Properties and Reasons:
Distributive Property: The 2 distributes to both terms inside the parentheses.
Combining Like Terms: 2x + 16 = 2x + 8.
Step 1: Distribute the 2 on the left side of the equation.
2 * x + 2 * 8 = 2 * x + 8
This simplifies to:
2x + 16 = 2x + 8
Step 2: Simplify the equation by combining like terms on both sides.
Since the variables and constants are the same on both sides of the equation, we can subtract 2x from both sides to eliminate the variable:
2x - 2x + 16 = 2x - 2x + 8
This simplifies to:
16 = 8
The equation is not true.
Conclusion: The equation 2(x+8) = 2x + 8 has no solution because the statement 16 = 8 is false.
To solve the equation 2(x+8) = 2x + 8, we need to simplify both sides of the equation and find the value of x.
Step 1: Distribute the 2 on the left side of the equation:
2(x+8) = 2x + 8
2x + 16 = 2x + 8
Step 2: Now, let's isolate the variable x by subtracting 2x from both sides of the equation:
2x + 16 - 2x = 2x + 8 - 2x
16 = 8
After simplifying, we can see that 16 is not equal to 8. Therefore, there is no solution to this equation.