Q2. - Algebra 1

Question

Solve each inequality. Then graph it on a number line. 

$m+2\ge 6$

Step-by-Step Solution

Answer

The required value of x is $\left[4,\infty \right)$. The graph on the number line is,

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{ or }\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b\le c\Rightarrow b\pm a\le c\pm a \\ 2.b\le c\Rightarrow ab\le ac,\text{ if }a>0 \\ 3.b\le c\Rightarrow ab\ge ac,\text{ if }a<0 \end{gathered}$$

Step 2. Solve the inequality for x .

In order to solve the inequality:

$m+2\ge 6$ 

Subtract 2 from both sides of the inequality, as

 $$\begin{gathered} m+2\ge 6 \\ m+2-2\ge 6-2 \\ m\ge 4 \end{gathered}$$

Thus, the solution of the given inequality is every number greater than or equal to 4, this can be represented in the interval form, as $\left[4,\infty \right)$.

Step 3. Plot the graph on the number line .

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point 4 is not strict, so use a solid circle at point 4. And the solution interval at right endpoint $\infty$, thus every point greater than 4 is in the solution interval of given inequality. The graph of the solution of inequality is shown below: