# Question Video: Finding the Solution Set to a Linear Equation That Includes a Radical Mathematics

Which of the following is the solution set of the equation 2𝑥 + 2√3 = 2 in ℝ? [A] {1 + √3} [B] {1 − √3} [C] {2 + √3} [D] {2 − √3} [E] {4 − √3}

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### Video Transcript

Which of the following is the solution set of the equation two 𝑥 plus two root three equals two in the real numbers? Is it (A) one plus root three, (B) one minus root three, (C) two plus root three, (D) two minus root three, or (E) four minus root three?

In this question, we need to solve a linear equation in the form 𝑎𝑥 plus 𝑏 equals 𝑐, where 𝑎, 𝑏, and 𝑐 are constants. We solve the two-step equation two 𝑥 plus two root three equals two by firstly isolating the 𝑥-term. To do this, we subtract two root three from both sides. This is the same as adding the additive inverse of 𝑏 to both sides of the general equation. When we do this, the left-hand side becomes two 𝑥. And on the right-hand side, we have two minus two root three.

Our next step is to divide both sides of the equation by two. This is the coefficient of 𝑥. On the left-hand side, the twos cancel, leaving us with 𝑥. And on the right-hand side, we are left with one minus root three. We can therefore conclude that the solution set of the equation two 𝑥 plus two root three equals two is option (B) one minus root three.