Answer :
To determine which equation has the solution \( x = 4 \), we will substitute \( x = 4 \) into each given equation and check if the equation holds true.
1. First equation:
[tex]\[ 4x = 20 \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4(4) = 20 \][/tex]
[tex]\[ 16 \neq 20 \][/tex]
This equation does not hold true for \( x = 4 \).
2. Second equation:
[tex]\[ \frac{x}{2} = 8 \][/tex]
Substitute \( x = 4 \):
[tex]\[ \frac{4}{2} = 8 \][/tex]
[tex]\[ 2 \neq 8 \][/tex]
This equation does not hold true for \( x = 4 \).
3. Third equation:
[tex]\[ x + 8 = 3x \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4 + 8 = 3(4) \][/tex]
[tex]\[ 12 = 12 \][/tex]
This equation holds true for \( x = 4 \).
4. Fourth equation:
[tex]\[ x = \frac{x + 5}{2} \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4 = \frac{4 + 5}{2} \][/tex]
[tex]\[ 4 = \frac{9}{2} \][/tex]
[tex]\[ 4 \neq \frac{9}{2} \][/tex]
This equation does not hold true for \( x = 4 \).
After substituting \( x = 4 \) into each equation, we find that the third equation \( x + 8 = 3x \) is the only one that holds true. Therefore, the equation that has the solution \( x = 4 \) is:
[tex]\[ x + 8 = 3 x \][/tex]
1. First equation:
[tex]\[ 4x = 20 \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4(4) = 20 \][/tex]
[tex]\[ 16 \neq 20 \][/tex]
This equation does not hold true for \( x = 4 \).
2. Second equation:
[tex]\[ \frac{x}{2} = 8 \][/tex]
Substitute \( x = 4 \):
[tex]\[ \frac{4}{2} = 8 \][/tex]
[tex]\[ 2 \neq 8 \][/tex]
This equation does not hold true for \( x = 4 \).
3. Third equation:
[tex]\[ x + 8 = 3x \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4 + 8 = 3(4) \][/tex]
[tex]\[ 12 = 12 \][/tex]
This equation holds true for \( x = 4 \).
4. Fourth equation:
[tex]\[ x = \frac{x + 5}{2} \][/tex]
Substitute \( x = 4 \):
[tex]\[ 4 = \frac{4 + 5}{2} \][/tex]
[tex]\[ 4 = \frac{9}{2} \][/tex]
[tex]\[ 4 \neq \frac{9}{2} \][/tex]
This equation does not hold true for \( x = 4 \).
After substituting \( x = 4 \) into each equation, we find that the third equation \( x + 8 = 3x \) is the only one that holds true. Therefore, the equation that has the solution \( x = 4 \) is:
[tex]\[ x + 8 = 3 x \][/tex]
