To determine how many solutions there are to the equation [tex]\( 5x + 15 = 5(x + 4) \)[/tex], let's go through the steps to simplify and solve it.
First, start with the given equation:
[tex]\[ 5x + 15 = 5(x + 4) \][/tex]
Distribute the 5 on the right side of the equation:
[tex]\[ 5x + 15 = 5x + 20 \][/tex]
Next, we will aim to isolate the variable [tex]\( x \)[/tex] by moving all terms involving [tex]\( x \)[/tex] to one side and constants to the other side. Subtract [tex]\( 5x \)[/tex] from both sides:
[tex]\[ 5x + 15 - 5x = 5x + 20 - 5x \][/tex]
This simplifies to:
[tex]\[ 15 = 20 \][/tex]
At this point, we observe that we have a statement that is not true ([tex]\( 15 \neq 20 \)[/tex]). This indicates that the equation is inconsistent and has no possible values of [tex]\( x \)[/tex] that satisfy the equation.
Therefore, the equation [tex]\( 5x + 15 = 5(x + 4) \)[/tex] has:
B. No solution
