To determine which expressions can be added to \(3x\) to result in the expression \(5x - 8\), we need to set up an equation. We are looking for expressions \(E\) such that:
\[ 3x + E = 5x - 8 \]
To find \(E\), we can rearrange the equation:
\[ E = (5x - 8) - 3x \] \[ E = 5x - 3x - 8 \] \[ E = 2x - 8 \]
So, the expression that can be added to \(3x\) to result in \(5x - 8\) is \(2x - 8\).
Now, let's evaluate each of the given options:
-
\(5x + 8\):
\(3x + (5x + 8) = 8x + 8\) (not equal to \(5x - 8\)) -
\(2x - 8\):
\(3x + (2x - 8) = 5x - 8\) (this is a match) -
\(5x - 8\):
\(3x + (5x - 8) = 8x - 8\) (not equal to \(5x - 8\)) -
\(-8 + 2x\):
\(3x + (-8 + 2x) = 5x - 8\) (this is a match since it is equivalent to \(2x - 8\)) -
\(-2x + 8\):
\(3x + (-2x + 8) = x + 8\) (not equal to \(5x - 8\))
Only the following expressions can be added to \(3x\) to yield \(5x - 8\):
- \(2x - 8\)
- \(-8 + 2x\)
So the correct answers are:
- \(2x - 8\)
- \(-8 + 2x\)
1 answer