Answer :
Sure, let's use the distributive property to match the equivalent expressions for [tex]\(-7(-4 + x)\)[/tex].
### Original Expression:
[tex]\[ -7(-4 + x) \][/tex]
### Applying the Distributive Property:
Using the distributive property, we need to multiply [tex]\(-7\)[/tex] by both terms inside the parentheses.
#### Step-by-Step:
1. Distribute [tex]\(-7\)[/tex] to [tex]\(-4\)[/tex]:
[tex]\[ -7 \times (-4) = 28 \][/tex]
2. Distribute [tex]\(-7\)[/tex] to [tex]\(x\)[/tex]:
[tex]\[ -7 \times x = -7x \][/tex]
3. Combine the results:
[tex]\[ 28 - 7x \][/tex]
So, the expression [tex]\(-7(-4 + x)\)[/tex] simplifies to:
[tex]\[ 28 - 7x \][/tex]
Now, let's compare this with the given expressions:
1. 7:
This is just a constant and does not match [tex]\(28 - 7x\)[/tex].
2. 28 + 7x:
The expression is not equivalent to [tex]\(28 - 7x\)[/tex] because the sign of [tex]\(7x\)[/tex] is incorrect. This expression has a positive [tex]\(7x\)[/tex] instead of negative.
3. 7(4 + x):
Let's also apply the distributive property here:
[tex]\[ 7 \times 4 + 7 \times x = 28 + 7x \][/tex]
This is the previous incorrect expression.
4. -7(4 - x):
Distribute [tex]\(-7\)[/tex] over the terms inside the parentheses:
[tex]\[ -7 \times 4 + (-7) \times (-x) = -28 + 7x \][/tex]
This expression is not equivalent to [tex]\(28 - 7x\)[/tex].
5. 7(-4 - x):
Distribute [tex]\(7\)[/tex] over the terms inside the parentheses:
[tex]\[ 7 \times (-4) + 7 \times (-x) = -28 - 7x \][/tex]
This expression is not equivalent to [tex]\(28 - 7x\)[/tex].
From these comparisons, we can conclude that the expression [tex]\(-7(-4 + x)\)[/tex] is equivalent to:
[tex]\[ 28 - 7x \][/tex]
Thus, the correct matching expression is 28 - 7x.
### Original Expression:
[tex]\[ -7(-4 + x) \][/tex]
### Applying the Distributive Property:
Using the distributive property, we need to multiply [tex]\(-7\)[/tex] by both terms inside the parentheses.
#### Step-by-Step:
1. Distribute [tex]\(-7\)[/tex] to [tex]\(-4\)[/tex]:
[tex]\[ -7 \times (-4) = 28 \][/tex]
2. Distribute [tex]\(-7\)[/tex] to [tex]\(x\)[/tex]:
[tex]\[ -7 \times x = -7x \][/tex]
3. Combine the results:
[tex]\[ 28 - 7x \][/tex]
So, the expression [tex]\(-7(-4 + x)\)[/tex] simplifies to:
[tex]\[ 28 - 7x \][/tex]
Now, let's compare this with the given expressions:
1. 7:
This is just a constant and does not match [tex]\(28 - 7x\)[/tex].
2. 28 + 7x:
The expression is not equivalent to [tex]\(28 - 7x\)[/tex] because the sign of [tex]\(7x\)[/tex] is incorrect. This expression has a positive [tex]\(7x\)[/tex] instead of negative.
3. 7(4 + x):
Let's also apply the distributive property here:
[tex]\[ 7 \times 4 + 7 \times x = 28 + 7x \][/tex]
This is the previous incorrect expression.
4. -7(4 - x):
Distribute [tex]\(-7\)[/tex] over the terms inside the parentheses:
[tex]\[ -7 \times 4 + (-7) \times (-x) = -28 + 7x \][/tex]
This expression is not equivalent to [tex]\(28 - 7x\)[/tex].
5. 7(-4 - x):
Distribute [tex]\(7\)[/tex] over the terms inside the parentheses:
[tex]\[ 7 \times (-4) + 7 \times (-x) = -28 - 7x \][/tex]
This expression is not equivalent to [tex]\(28 - 7x\)[/tex].
From these comparisons, we can conclude that the expression [tex]\(-7(-4 + x)\)[/tex] is equivalent to:
[tex]\[ 28 - 7x \][/tex]
Thus, the correct matching expression is 28 - 7x.
