Question

solve the inequality both algebraically and graphically. draw a number line graph of the solution and give interval notation. (\frac{x - 5}{2} < \frac{34}{5})
the solution as an inequality is (square).
(type an inequality. simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Eliminate denominator

Multiply both sides by 2:
$x - 5 < \frac{34}{5} \times 2$
$x - 5 < \frac{68}{5}$

Step2: Isolate $x$

Add 5 to both sides (rewrite 5 as $\frac{25}{5}$):
$x < \frac{68}{5} + \frac{25}{5}$
$x < \frac{93}{5}$
$x < 18.6$

Step3: Interval notation setup

The solution includes all real numbers less than $\frac{93}{5}$, so in interval notation this is $(-\infty, \frac{93}{5})$. For the number line: draw an open circle at $\frac{93}{5}$ (or 18.6) and shade all values to the left of this point.

Answer:

Algebraic solution: $x < \frac{93}{5}$
Interval notation: $(-\infty, \frac{93}{5})$
Graph description: Open circle at $\frac{93}{5}$ (18.6) on the number line, shading extending to the left towards negative infinity.