The Correct Answer and Explanation is:
Based on the problem shown in the image, the correct simplified expression is -6x + 4.
Here is a detailed explanation of how to arrive at this answer.
To find an expression that is equivalent to 16 – 5x – 12 – x, you need to simplify it by combining the “like terms”. Like terms are the parts of an algebraic expression that have the same variable raised to the same power. In this problem, we have two kinds of like terms: constant terms and terms containing the variable x.
First, identify and group the constant terms. These are the numbers without any variables attached. In the expression 16 – 5x – 12 – x, the constants are 16 and -12.
Next, identify and group the terms that contain the variable x. These are -5x and -x. The commutative property of addition allows us to rearrange the expression to group these like terms together without changing its value: (16 – 12) + (-5x – x).
Now, perform the arithmetic for each group of like terms.
For the constant terms, you subtract 12 from 16:
16 – 12 = 4
For the variable terms, you combine -5x and -x. It is important to remember that -x is the same as -1x. To combine these terms, you add their coefficients, which are the numbers in front of the variable. So, you calculate -5 + (-1) or simply -5 – 1.
-5 – 1 = -6
This gives you a combined variable term of -6x.
Finally, put the simplified parts back together. You have the 4 from the constants and the -6x from the variable terms. This creates the final, simplified expression: -6x + 4.
This expression is equivalent to the original one because it will produce the same numerical result for any value you substitute for x.
