How do you solve and graph 1/2<=c-3/4?

Dec 19, 2017

See a solution process below:

Explanation:

Add $\textcolor{red}{\frac{3}{4}}$ to each side of the inequality to solve for $c$ while keeping the inequality balanced:

$\frac{1}{2} + \textcolor{red}{\frac{3}{4}} \le c - \frac{3}{4} + \textcolor{red}{\frac{3}{4}}$

$\left(\frac{2}{2} \times \frac{1}{2}\right) + \textcolor{red}{\frac{3}{4}} \le c - 0$

$\frac{2}{4} + \textcolor{red}{\frac{3}{4}} \le c$

$\frac{2 + 3}{4} \le c$

$\frac{5}{4} \le c$

We can reverse or "flip" the entire inequality to state the solution in terms of $c$:

$c \ge \frac{5}{4}$

To graph this we will draw a vertical line at $\frac{5}{4}$ on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x >= 5/4 [-1, 3, -1, 1]}