Question

Solve the linear Inequality. Express the solution using interval notation and graph the solution set.

$2x+1<0$

Short answer

The solution set of given inequality is $x<-\frac{1}{2}$that is $x\in (-\infty ,-\frac{1}{2})$.

Step-by-step solution

Step-1. Determining the solution to Inequality.

$2x+1<0$

$2x+1-1<0-1$ (Subtract)

$2x<-1$ (Simplify)

$\frac{2x}{2}<-\frac{1}{2}$ (Multiply by)

$x<-\frac{1}{2}$ (Simplify)

Step-2. Expressing the solution set in Interval Notation.

The solution set consists of all numbers less than $-\frac{1}{2}$. In other words, the solution of the inequality is the interval$(-\infty ,-\frac{1}{2})$

Step-3. Graphing the solution set.

$x<-\frac{1}{2}$

$x\in (-\infty ,-\frac{1}{2})$