Questions: Solve the inequality (1/2-m/6<7/12) and then graph and give the solution in interval notation: Inequality notation: Graph the solution below: Interval notation:

Solution Steps

The given inequality is $\frac{1}{2} - \frac{m}{6} < \frac{7}{12}$. The denominators are 2, 6, and 12. The least common multiple of these numbers is 12. Multiply each term by 12: $12(\frac{1}{2}) - 12(\frac{m}{6}) < 12(\frac{7}{12})$ $6 - 2m < 7$

Subtract 6 from both sides: $6 - 2m - 6 < 7 - 6$ $-2m < 1$

Divide both sides by -2. Remember to reverse the inequality sign when dividing or multiplying by a negative number. $\frac{-2m}{-2} > \frac{1}{-2}$ $m > -\frac{1}{2}$

The inequality notation is $m > -\frac{1}{2}$.

Since $m > -\frac{1}{2}$, the graph starts at $-\frac{1}{2}$ with an open circle (because the inequality is strictly greater than) and extends to the right.

<------------------|-------------------> -4 -3 -2 -1 0 1 2 3 o

The open circle is at $-\frac{1}{2} = -0.5$ which is between -1 and 0.

The interval notation is $(-\frac{1}{2}, \infty)$.

Final Answer