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.