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Is [tex]x=-4[/tex] a valid solution to this linear equation?

[tex]\[ 2x + 9(x-1) = 8(2x + 2) - 5 \][/tex]

A. No. When -4 is substituted for the variable, the result is a true statement.
B. No. When -4 is substituted for the variable, the result is a false statement.
C. Yes. When -4 is substituted for the variable, the result is a true statement.
D. Yes. When -4 is substituted for the variable, the result is a false statement.

Sagot :

GinnyAnsweridn
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.
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