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Let’s check out your problem:
Simplify to create an equivalent expression.
\newline
8
−
4
(
−
x
+
5
)
8-4(-x+5)
8
−
4
(
−
x
+
5
)
\newline
Choose
1
1
1
answer:
\newline
(A)
4
x
−
12
4x-12
4
x
−
12
\newline
(B)
−
4
x
−
12
-4x-12
−
4
x
−
12
\newline
(C)
4
x
+
13
4x+13
4
x
+
13
\newline
(D)
4
x
+
5
4x+5
4
x
+
5
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Home
Math Problems
Algebra 1
Simplify variable expressions involving like terms and the distributive property
Full solution
Q.
Simplify to create an equivalent expression.
\newline
8
−
4
(
−
x
+
5
)
8-4(-x+5)
8
−
4
(
−
x
+
5
)
\newline
Choose
1
1
1
answer:
\newline
(A)
4
x
−
12
4x-12
4
x
−
12
\newline
(B)
−
4
x
−
12
-4x-12
−
4
x
−
12
\newline
(C)
4
x
+
13
4x+13
4
x
+
13
\newline
(D)
4
x
+
5
4x+5
4
x
+
5
Distribute
−
4
-4
−
4
:
First, we need to distribute the
−
4
-4
−
4
across the terms inside the parentheses. This means we will multiply
−
4
-4
−
4
by
−
x
-x
−
x
and then
−
4
-4
−
4
by
5
5
5
.
Simplify terms:
Distributing
−
4
-4
−
4
across the terms inside the parentheses gives us
−
4
×
−
x
+
−
4
×
5
-4 \times -x + -4 \times 5
−
4
×
−
x
+
−
4
×
5
, which simplifies to
4
x
−
20
4x - 20
4
x
−
20
.
Add to
8
8
8
:
Now, we add the simplified expression
4
x
−
20
4x - 20
4
x
−
20
to the
8
8
8
that is outside the parentheses. This means we will calculate
8
−
(
4
x
−
20
)
8 - (4x - 20)
8
−
(
4
x
−
20
)
.
Combine like terms:
Subtracting
4
x
−
20
4x - 20
4
x
−
20
from
8
8
8
gives us
8
−
4
x
+
20
8 - 4x + 20
8
−
4
x
+
20
, because subtracting a negative is the same as adding a positive.
Add constants:
Finally, we combine the like terms, which are the constants
8
8
8
and
20
20
20
. This gives us
−
4
x
+
(
8
+
20
)
-4x + (8 + 20)
−
4
x
+
(
8
+
20
)
.
Final expression:
Adding
8
8
8
and
20
20
20
gives us
28
28
28
. So the expression simplifies to
−
4
x
+
28
-4x + 28
−
4
x
+
28
.
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\newline
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