To find the expressions equivalent to \( 0.6(-7 - 1.2x) \), let's first simplify this expression:
- Distribute \( 0.6 \): \[ 0.6(-7 - 1.2x) = 0.6(-7) + 0.6(-1.2x) = -4.2 - 0.72x \]
Now we have \( -4.2 - 0.72x \).
Next, we can analyze the given expressions to see if any are equivalent to this result:
-
Expression 1: \( -0.72x + (-4.2) \)
This simplifies to \( -4.2 - 0.72x \) which is equivalent. -
Expression 2: \( 0.6(-7) - 0.6(-1.2x) \)
We can compute this: \[ 0.6(-7) = -4.2 \quad \text{and} \quad -0.6(-1.2x) = 0.72x \] Thus, \( -4.2 + 0.72x \) is not equivalent. -
Expression 3: \( -4.2 - 1.2x \)
This is not equivalent because it has \( -1.2x \) instead of \( -0.72x \). -
Expression 4: \( -4(0.18x + 1.05) \)
This expands to: \[ -4(0.18x) - 4(1.05) = -0.72x - 4.2 \] This is equivalent since it simplifies to \( -4.2 - 0.72x \). -
Expression 5: \( 0.6(-7) + 0.6(-1.2x) \)
We compute this again: \[ 0.6(-7) = -4.2 \quad \text{and} \quad 0.6(-1.2x) = -0.72x \] Thus, this results in \( -4.2 - 0.72x \), which is equivalent. -
Expression 6: \( -4.2 - 0.72x \)
This is identical to what we previously calculated, so it is equivalent. -
Expression 7: \( -4.2 + 0.72x \)
This is not equivalent because it has \( +0.72x \) instead of \( -0.72x \).
In conclusion, the expressions that are equivalent to \( 0.6(-7 - 1.2x) \) are:
- \( -0.72x + (-4.2) \)
- \( -4(0.18x + 1.05) \)
- \( 0.6(-7) + 0.6(-1.2x) \)
- \( -4.2 - 0.72x \)