Which of the following is equivalent to the inequality 7>-3x>-12?
a. -7<x<12
b. 7/3 <x<4
c. -7/3<x<4
d. -4<x<-7/3
e. -4<x<7
please answer and explain
7>-3x>-12
divide by -3 (changes direction of inequality)
-7/3 < x < 4
(c)
-w>7
To solve the inequality 7 > -3x > -12, we need to divide each part of the inequality by -3. However, when dividing an inequality expression by a negative number, we must reverse the direction of the inequality signs.
Divide each part of the inequality by -3:
7/-3 < x < -12/-3
This simplifies to:
-7/3 < x < 4
The equivalent inequality is given by the answer choice:
c. -7/3 < x < 4
To explain the steps further:
1. Start with the original inequality: 7 > -3x > -12
2. Divide each part of the inequality by -3: (-3x)/-3 > (-12)/-3
3. Simplify: x < 4 and -7 > x
4. Swap the positions of the terms to have x as the subject: -7 < x < 4
5. Convert the inequality to fraction form: -7/1 < x < 4/1
6. Simplify the fractions: -7/1 < x < 4/1
7. Denote proper fraction notation: -7/3 < x < 4/1
8. Since the denominator of the fraction is 1, it is often not included, resulting in -7/3 < x < 4.