Q. 2 PT - Algebra 1

Question

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

$\mathbf{6}\mathit{p}\mathbf{\ge }\mathbf{5}\mathit{p}\mathbf{-}\mathbf{3}$

Step-by-Step Solution

Answer

The solution of the given inequality $6p\ge 5p-3$ is $\mathit{p}\mathbf{\ge }\mathbf{-}\mathbf{3}$.

The graph of the solution of the given inequality $6p\ge 5p-3$ that is graph of $p\ge -3$ is:

Step 1. Write the subtraction property of inequalities.

The subtraction property of inequalities states that if the same number is subtracted from each side of a true inequality, the resulting inequality is also true that is:

1. If $a>b$, then $a-c>b-c$.
2. If $a<b$, then .$a-c<b-c$.

Step 2. Solve the given inequality 6 p &#8805; 5 p &#8722; 3 .

The solution of the given inequality $6p\ge 5p-3$ is:

$\begin{array}{c}6p\ge 5p-3\\ 6p-5p\ge 5p-3-5p\left(\text{by using subtraction property of inequality}\right)\\ p\ge 5p-5p-3\\ p\ge -3\end{array}$

 Therefore, the solution of the given inequality $6p\ge 5p-3$ is $p\ge -3$.

Step 3. Draw the graph of the inequality p &#8805; &#8722; 3 .

The graph of the solution of the given inequality $6p\ge 5p-3$ that is graph of $p\ge -3$ is:

It can be noticed that at $p=-3$, there is closed circle because $-3$ is included in the inequality $p\ge -3$.