Select all values of [tex]$x$[/tex] that are solutions to the equation [tex]$(x-5)(7x-21)=0$[/tex].

A. -7
B. -5
C. -3
D. 0
E. 3
F. 5



Answer :

To solve the equation [tex]\((x - 5)(7x - 21) = 0\)[/tex], we use the zero product property, which states that if a product of two factors is zero, at least one of the factors must be zero.

First, we set each factor equal to zero and solve for [tex]\( x \)[/tex].

1. Factor 1: [tex]\( x - 5 = 0 \)[/tex]
[tex]\[ x - 5 = 0 \][/tex]
Adding 5 to both sides to solve for [tex]\( x \)[/tex],
[tex]\[ x = 5 \][/tex]

2. Factor 2: [tex]\( 7x - 21 = 0 \)[/tex]
[tex]\[ 7x - 21 = 0 \][/tex]
Adding 21 to both sides,
[tex]\[ 7x = 21 \][/tex]
Dividing both sides by 7,
[tex]\[ x = 3 \][/tex]

So the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\((x - 5)(7x - 21) = 0\)[/tex] are [tex]\( x = 5 \)[/tex] and [tex]\( x = 3 \)[/tex].

Therefore, the correct answers are:
E [tex]\( 3 \)[/tex]
F [tex]\( 5 \)[/tex]