Question

Solve for x.5x−19≤1 OR −4x+3<−6

A) x ≥ 4
B) 9/4C) x> − 9/4
D) There are no solutions

Answer 1

To solve the given system of inequalities, solve each inequality separately and find the intersection of the solution sets x ≤ 4 and x > 9/4.

Step-by-step explanation:

To solve the given system of inequalities, you can solve each inequality separately and find the intersection of the solution sets.

First inequality:

5x - 19 ≤ 1

Add 19 to both sides: 5x ≤ 20

Divide both sides by 5: x ≤ 4

Second inequality:

-4x + 3 < -6

Subtract 3 from both sides: -4x < -9

Divide both sides by -4 (Remember to flip the inequality sign when dividing by a negative number): x > 9/4

Now, find the intersection of the solution sets:

x ≤ 4 AND x > 9/4

The only values of x that satisfy both inequalities are x > 9/4. Therefore, the solution is:

x > 9/4