Question

solve the inequality. graph the solution on a number line and represent the solution in interval notation when possible.
$t+\frac{1}{8}>\frac{3}{4}t$
a. the solution is $t >-\frac{1}{2}$ (type an inequality. simplify your answer.)
b. the solution is all real numbers
c. there is no solution
choose the correct graph of the inequality
a. number - line graph options
b. number - line graph options
c. number - line graph options
d. number - line graph options
e. number - line graph options
f. number - line graph options

Explanation:

Step1: Move terms with t to one - side

$t-\frac{3}{4}t>-\frac{1}{8}$

Step2: Combine like - terms

$\frac{4t - 3t}{4}>-\frac{1}{8}$
$\frac{t}{4}>-\frac{1}{8}$

Step3: Solve for t

$t>-\frac{1}{8}\times4$
$t >-\frac{1}{2}$

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

For the graph, since $t>-\frac{1}{2}$, we have an open - circle at $-\frac{1}{2}$ and the line extends to the right.

Answer:

A. The solution is $t>-\frac{1}{2}$; C. (the graph with an open - circle at $-\frac{1}{2}$ and the line extending to the right)