Which is the solution set of the compound inequality [tex]$3.5 x-10\ \textgreater \ -3$[/tex] and [tex]$8 x-8\ \textless \ 38$[/tex]?
A. [tex]$-2\ \textless \ x\ \textless \ 3 \frac{3}{4}$[/tex]
B. [tex]$-2\ \textless \ x\ \textless \ 6$[/tex]
C. [tex]$2\ \textless \ x\ \textless \ 6$[/tex]
D. [tex]$2\ \textless \ x\ \textless \ 3 \frac{3}{4}$[/tex]
Answer (2)
The solution to the compound inequality is found by solving each inequality separately and then finding their intersection. The final solution set is given by the range 2 < x < 5 4 3 . Therefore, the correct answer is option D.
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Solve the first inequality -3"> 3.5 x − 10 > − 3 to get 2"> x > 2 .
Solve the second inequality 8 x − 8 < 38 to get x < 5.75 .
Find the intersection of the two solution sets: 2 < x < 5.75 .
The solution set is \boxed{2 -3 and 8 x − 8 < 38 . We need to find the solution set for x that satisfies both inequalities.
Solving the First Inequality First, let's solve the inequality -3"> 3.5 x − 10 > − 3 . Add 10 to both sides: 7"> 3.5 x > 7
Divide both sides by 3.5: \frac{7}{3.5} = 2"> x > 3.5 7 = 2
Solving the Second Inequality Now, let's solve the inequality 8 x − 8 < 38 . Add 8 to both sides: 8 x < 46
Divide both sides by 8: x < 8 46 = 4 23 = 5.75 = 5 4 3
Finding the Intersection We need to find the intersection of the solution sets 2"> x > 2 and x < 5.75 . This means 2 < x < 5.75 . Since 5.75 = 5 4 3 , we have 2 < x < 5 4 3 . The given options are: $-2
