To determine which equation is true for [tex]\( x = 15 \)[/tex], we will evaluate each option step-by-step.
Option A:
[tex]\[ 2(x + 3) = 40 \][/tex]
Substitute [tex]\( x = 15 \)[/tex]:
[tex]\[ 2(15 + 3) = 2 \times 18 = 36 \][/tex]
This simplifies to:
[tex]\[ 36 \neq 40 \][/tex]
So, Option A is not correct.
Option B:
[tex]\[ 2(x - 5) = 30 \][/tex]
Substitute [tex]\( x = 15 \)[/tex]:
[tex]\[ 2(15 - 5) = 2 \times 10 = 20 \][/tex]
This simplifies to:
[tex]\[ 20 \neq 30 \][/tex]
So, Option B is not correct.
Option C:
[tex]\[ 2(x + 5) = 40 \][/tex]
Substitute [tex]\( x = 15 \)[/tex]:
[tex]\[ 2(15 + 5) = 2 \times 20 = 40 \][/tex]
This simplifies to:
[tex]\[ 40 = 40 \][/tex]
So, Option C is correct.
Option D:
[tex]\[ x + 2x = 30 \][/tex]
Substitute [tex]\( x = 15 \)[/tex]:
[tex]\[ 15 + 2 \times 15 = 15 + 30 = 45 \][/tex]
This simplifies to:
[tex]\[ 45 \neq 30 \][/tex]
So, Option D is not correct.
Option E:
[tex]\[ 3x - x = 45 \][/tex]
Substitute [tex]\( x = 15 \)[/tex]:
[tex]\[ 3 \times 15 - 15 = 45 - 15 = 30 \][/tex]
This simplifies to:
[tex]\[ 30 \neq 45 \][/tex]
So, Option E is not correct.
After evaluating all the options, we see that only Option C is correct.
Therefore, the correct answer is:
C. [tex]\( 2(x + 5) = 40 \)[/tex]
