Question

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

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

Short 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-by-step solution

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 6p≥5p−3.

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

$\begin{array}{c}6p\ge 5p-3\\ 6p-5p\ge 5p-3-5p\left(\text{byusingsubtractionpropertyofinequality}\right)\\ p\ge 5p-5p-3\\ p\ge -3\end{array}$

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

Step 3. Draw the graph of the inequality p≥−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 $p\ge -3$.