To determine if [tex]\( x = -4 \)[/tex] is a valid solution for the given linear equation:
[tex]\[ 2x + 9(x - 1) = 8(2x + 2) - 5 \][/tex]
we need to substitute [tex]\( x = -4 \)[/tex] into the equation and verify whether both sides of the equation are equal.
### Step-by-Step Solution:
1. Substitute [tex]\( x = -4 \)[/tex] into the left-hand side (LHS) of the equation:
[tex]\[
2x + 9(x - 1)
\][/tex]
Substitute [tex]\( x = -4 \)[/tex]:
[tex]\[
2(-4) + 9((-4) - 1)
\][/tex]
2. Simplify the LHS:
[tex]\[
2(-4) + 9(-5) = -8 - 45 = -53
\][/tex]
3. Next, Substitute [tex]\( x = -4 \)[/tex] into the right-hand side (RHS) of the equation:
[tex]\[
8(2x + 2) - 5
\][/tex]
Substitute [tex]\( x = -4 \)[/tex]:
[tex]\[
8(2(-4) + 2) - 5
\][/tex]
4. Simplify the RHS:
[tex]\[
8(-8 + 2) - 5 = 8(-6) - 5 = -48 - 5 = -53
\][/tex]
5. Compare the LHS and RHS:
[tex]\[
\text{LHS} = -53
\][/tex]
[tex]\[
\text{RHS} = -53
\][/tex]
Since both sides of the equation are equal when [tex]\( x = -4 \)[/tex], this means:
[tex]\[ -53 = -53 \][/tex]
Hence, substituting [tex]\( x = -4 \)[/tex] results in a true statement. Therefore, the correct answer is:
Yes. When [tex]\( -4 \)[/tex] is substituted for the variable, the result is a true statement.
