Q. 27 - Algebra 2

Question

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

 $\mathbf{5}\left(\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{5}\right)\mathbf{+}\mathbf{x}<\mathbf{2}\left(\mathbf{4}\mathbf{x}\mathbf{-}\mathbf{1}\right)\mathbf{+}\mathbf{1}$

Step-by-Step Solution

Answer

Solution set of inequality is $\left(\mathbf{-}\infty \mathbf{,}\mathbf{3}\right)$.

Solution set on number line is 

Step 1. Write properties of inequality.

Properties of inequalities are written in following table:

Step 2. Solve 5 3 x - 5 + x &#60; 2 4 x - 1 + 1 .

To solve given inequality, use subtraction and division properties of inequality. Expand the parentheses on each side. Subtract 25 and then $8x$ from each side then divide each side by 8 and simplify.

$\begin{array}{c}15x-25+x<8x-2+1\\ 16x-25+25<8x-1+25\\ 16x-8x<8x+24-8x\\ \frac{8x}{8}<\frac{24}{8}\\ x<3\end{array}$

Thus, solution is $x<3$.

Step 3. Describe solution set in interval notation.

As solution set of the inequality is all real numbers less than 3.

Write the solution set in interval notation.

$\left(-\infty ,3\right)$

Step 4. Graph the solution set.

Open circle on 3 shows this point is excluded in the solution set.