## College Algebra (10th Edition)

RECALL: (1) The Multiplication Property of Inequality states that if a positive number is multiplied to each side of an inequality, the inequality's direction/sense does not change. Thus, if $a \gt b$ and $c\gt 0$, then $ac \gt bc$. (2) The addition property of inequalities states that If $a \ge b$, then $a+c \ge b+c$ Use the rule in (2) above by adding $1$ and $-x$ on each side to obtain: $\begin{array}{ccc} &3x-1+1+(-x) &\ge &3+x+1+(-x) \\&(3x-x)+(-1+1) &\ge &(x-x)+(3+1) \\&2x &\gt &4 \end{array}$ Use the rule in (1) above by multiplying $\frac{1}{2}$ on both sides of the inequality to obtain: $\begin{array}{ccc} &\frac{1}{2}(2x) &\ge &\frac{1}{2}(4) \\&x &\ge &2 \end{array}$ Thus, the solution set is $[2, +\infty)$. To graph this on a number line, plot a solid dot at $2$, and then shade the region to its right.