To find an expression that represents the difference when [tex]\(2x - 6\)[/tex] is subtracted from [tex]\(7x - 0.5\)[/tex], follow these steps:
1. Set up the expression for the difference:
We are given two expressions: [tex]\(7x - 0.5\)[/tex] and [tex]\(2x - 6\)[/tex]:
[tex]\[
(7x - 0.5) - (2x - 6)
\][/tex]
2. Distribute the negative sign across the second expression:
When subtracting [tex]\(2x - 6\)[/tex], distribute the negative sign:
[tex]\[
(7x - 0.5) - 2x + 6
\][/tex]
3. Combine like terms:
Combine the terms containing [tex]\(x\)[/tex] and the constant terms separately:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
7x - 2x = 5x
\][/tex]
- Combine the constant terms:
[tex]\[
-0.5 + 6 = 5.5
\][/tex]
4. Write the simplified expression:
Therefore, the simplified expression that represents the difference is:
[tex]\[
5x + 5.5
\][/tex]
Thus, the expression which represents the difference when [tex]\(2x - 6\)[/tex] is subtracted from [tex]\(7x - 0.5\)[/tex] in simplest terms is:
[tex]\[
5x + 5.5
\][/tex]
