# Question Video: Finding the Solution Set to a Linear Equation and Representing It on a Number Line Mathematics

Find, in ℝ, the solution set of the equation 2𝑥 + 3 = 5. Which of the following represents the solution of the equation on a number line? [A] Option A [B] Option B [C] Option C [D] Option D [E] Option E

02:14

### 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.