Q37. - Algebra 2

Question

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

37. $\frac{4x+2}{6}<\frac{2x+1}{3}$

Step-by-Step Solution

Answer

Inequality $\frac{4x+2}{6}<\frac{2x+1}{3}$ has no solution

In set-builder form, solution set is $\left\{\right\}$

On number line, no solution is there

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify 4 x + 2 6 &#60; 2 x + 1 3

To simplify given inequality, use properties of inequalities. Multiply both sides by same positive integer does not reverse the inequality. Subtract same numbers from both sides does not change the sign of inequality as shown below

$\begin{array}{c}\frac{4x+2}{6}<\frac{2x+1}{3}\\ \left(\frac{4x+2}{6}\right)\times 6<\left(\frac{2x+1}{3}\right)\times 6\\ 4x+2<4x+2\\ 4x-4x+2-2<4x-4x+2-2\\ 0<0\left(\text{false}\right)\end{array}$

Step 3 - Write solution set

On solving given inequality, a false statement is obtained.

So there is not solution to given inequality.

In set-builder form solution set is an empty set $\left\{\right\}$

Step 4 - Graph the solution set

As solution set of the inequality empty. So no solution on number line.