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How many solutions are there to the equation below?

[tex]\[ 5x + 15 = 5(x + 4) \][/tex]

A. Infinitely many solutions
B. No solution
C. One solution

Sagot :

GinnyAnsweridn
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
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