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{26}{5}\\)\\(\\)\\(\\)the solution as an inequality is \\(\square\\).\\(\\)\\((\text{type an inequality. simplify your answer. use integers or fractions for any numbers in the expression.})\\)\\(\\)the solution in interval notation is \\(\square\\).\\(\\)\\((\text{type your answer in interval notation. use integers or fractions for any numbers in the expression.})\\)\\(\\)choose the correct graph of the solution below.\\(\\)\\(\bigcirc\\) a. \\(\quad\bigcirc\\) b. \\(\\)\\(\bigcirc\\) c. \\(\quad\bigcirc\\) d. \\(\\)\\(\bigcirc\\) e. \\(\quad\bigcirc\\) f. \\(\\)\\(\bigcirc\\) g. \\(\quad\bigcirc\\) h.

Explanation:

Step1: Eliminate denominators via cross-multiplication

Multiply both sides by $2 \times 5 = 10$ to clear fractions:
$5(x-5) < 2 \times 26$

Step2: Expand and simplify the left side

Distribute the 5 on the left:
$5x - 25 < 52$

Step3: Isolate the variable term

Add 25 to both sides to move constants right:
$5x < 52 + 25$
$5x < 77$

Step4: Solve for $x$

Divide both sides by 5:
$x < \frac{77}{5}$
$x < 15.4$

Answer:

The solution as an inequality is $\boldsymbol{x < \frac{77}{5}}$ (or $x < 15.4$)
The solution in interval notation is $\boldsymbol{(-\infty, \frac{77}{5})}$
The correct graph is Option C (arrow pointing left from an open circle at 15.4, which aligns with the open circle just right of 15 on the number line, extending left indefinitely)