To answer this question, we need to solve the given inequality, and we can proceed as follows:
1. We have the following expression for the inequality:
[tex]-7x+14>-3x-6[/tex]2. We need to add 3x to both sides of the inequality:
[tex]\begin{gathered} -7x+3x+14>-3x+3x-6 \\ -7x+3x+14>-6 \\ -4x+14>-6 \end{gathered}[/tex]3. Now, we need to subtract 14 from both sides of the inequality as follows:
[tex]\begin{gathered} -4x+14-14>-6-14 \\ -4x>-20 \end{gathered}[/tex]4. Finally, we need to divide both sides by -4 as follows:
[tex]\begin{gathered} -\frac{4}{-4}x<-\frac{20}{-4} \\ x<5 \end{gathered}[/tex]Notice that we change the direction of the inequality since we divide it by a negative number.
Therefore, the solution for the inequality is any number less than 5, or, in interval notation:
[tex]\begin{gathered} (-\infty,5) \\ x<5 \end{gathered}[/tex]And since we have the following options, we can say that:
• -10 ---> It is part of the solution since -10 < 5.
,• 10 ---> It is NOT part of the solution since 10 > 5.
• -5 ---> Solution ---> -5 < 5
• 5 ---> It is NOT part of the solution 5 = 5, and we need x < 5.
,• -3 ---> Solution ---> -3 < 5
,• 3 ---> Solution ---> 3 < 5
,• 0 ---> Solution ---> 0 < 5
In summary, we have that the values that are solutions for the inequality are:
• -10
,• -5
,• -3
,• 3
,• 0