Question

Solve −5x−3≥2 and 4x−2≥5 and write the solution in interval notation. If there is no solution, type ∅.

Answer 1

Answer:

7/4≤x ≤-1

Step-by-step explanation:

Given the set of inequalities

−5x−3≥2 and 4x−2≥5

We are to write the solution in interval notation. We need to solve them individually first as shown;

For −5x−3≥2

add 3 to both sides

−5x−3+3≥2+3

-5x ≥5

divide both sides by -5 (note that dividing by a negative value will change the sense of the inequality sign)

-5x/-5 ≤5/-5

x ≤ -1

For the inequality 4x−2≥5;

add 2 to both sides

4x−2+2≥5+2

4x≥7

divide both sides by 4;

4x/4 ≥ 7/4

x≥7/4 or 7/4≤x

Combining 7/4≤x and x ≤ -1, the solution in interval notation is expressed as 7/4≤x ≤-1