Answer:
7/4≤x ≤-1
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