Question

Consider the inequality 15 x − 8 110≤− 9 310 . Part A

Solve the inequality 15 x − 8 110≤− 9 310 . Complete the sentence to describe how to graph the solution on a number line.
The solution can be graphed by plotting a closed/open circle at the number_____and shading the number line to the left/right of the circle.

Answer 1

To solve the inequality
`\( (15x - 8)/(110) \leq -(9)/(310) \)`, first multiply both sides by 110 to eliminate the denominator. Then, simplify and solve for x. Graph the solution by plotting a closed/open circle at the number representing the solution and shading to the left/right of the circle based on the inequality sign.

To solve the inequality
`\( (15x - 8)/(110) \leq -(9)/(310) \)`, begin by multiplying both sides by 110 to clear the fraction.

This yields
`\(15x - 8 \leq -(99)/(31)\)`.

Next, add 8 to both sides, resulting in
`\(15x \leq -(99)/(31) + (2480)/(31)\)`.

Further simplification gives
`\(15x \leq (2381)/(31)\)`.

Finally, divide both sides by 15 to find
`\(x \leq (2381)/(465)\)`.

The solution can be graphed on a number line by plotting a closed/open circle at
`\((2381)/(465)\)` and shading to the left of the circle, indicating values of x that satisfy the inequality.