Video Transcript
Find, in the set of real numbers,
the solution set of the equation two 𝑥 plus three is equal to five. Which of the following represents
the solution of the equation on a number line? Is it option (A), (B), (C), (D), or
(E)?
The first part of this question
wants us to solve a linear equation in the form 𝑎𝑥 plus 𝑏 is equal to 𝑐, where
𝑎, 𝑏, and 𝑐 are constants. In order to solve the equation two
𝑥 plus three equals five, we begin by subtracting three from both sides. And as five minus three is equal to
two, we are left with two 𝑥 equals two. Our next step is to divide through
by the coefficient of 𝑥, in this case two. As two 𝑥 divided by two is 𝑥 and
two divided by two is one, we have 𝑥 is equal to one. The solution set of the equation
two 𝑥 plus three equals five contains the solitary element one.
The second part of this question
asks us to identify the solution to the equation on a number line. Option (E) represents the solution
𝑥 is equal to eight. Option (D) is the solution 𝑥 is
equal to three. Option (C) is the solution 𝑥 is
equal to four. And option (B) represents the
solution 𝑥 is equal to two. Since the solution to our equation
was 𝑥 is equal to one, none of these options are correct. The number line that represents the
solution of the equation two 𝑥 plus three equals five is option (A). We have a solid dot representing
the single value one.
