The equation $\frac12 t = 10$ is an equation in one variable. Its solution is any value of $t$ that makes the equation true. Only $t=20$ meets that requirement, so 20 is the only solution.

The inequality $\frac12t >10$ is an inequality in one variable. Any value of $t$ that makes the inequality true is a solution. For instance, 30 and 48 are both solutions because substituting these values for $t$ produces true inequalities. $\frac12(30) >10$ is true, as is $\frac12(48) >10$. Because the inequality has a range of values that make it true, we sometimes refer to all the solutions as the solution set.

One way to find the solutions to an inequality is by reasoning. For example, to find the solution to $2p<8$, we can reason that if 2 times a value is less than 8, then that value must be less than 4. So a solution to $2p<8$ is any value of $p$ that is less than 4.

Another way to find the solutions to $2p<8$ is to solve the related equation $2p=8$. In this case, dividing each side of the equation by 2 gives $p=4$. This point, where $p$ is 4, is the boundary of the solution to the inequality.

To find out the range of values that make the inequality true, we can try values less than and greater than 4 in our inequality and see which ones make a true statement.

In general, the inequality is false when $p$ is greater than or equal to 4 and true when $p$ is less than 4.

We can represent the solution set to an inequality by writing an inequality, $p<4$, or by graphing on a number line. The ray pointing to the left represents all values less than 4.