Answer :
Sure, let's solve the inequality step by step:
Given inequality:
[tex]\[ 3(-x + 2) < 15 \][/tex]
1. Distribute the 3 inside the parentheses:
[tex]\[ 3 \cdot -x + 3 \cdot 2 < 15 \][/tex]
[tex]\[ -3x + 6 < 15 \][/tex]
2. Subtract 6 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -3x + 6 - 6 < 15 - 6 \][/tex]
[tex]\[ -3x < 9 \][/tex]
3. Divide both sides by -3 to solve for [tex]\( x \)[/tex]. Since we are dividing by a negative number, the inequality sign will flip:
[tex]\[ x > \frac{9}{-3} \][/tex]
[tex]\[ x > -3 \][/tex]
Therefore, the solution to the inequality is:
[tex]\[ \boxed{x > -3} \][/tex]
Comparing this to the choices given:
(A) [tex]\( x > 7 \)[/tex]
(B) [tex]\( x < 3 \)[/tex]
(C) [tex]\( x < -7 \)[/tex]
(D) [tex]\( x > -3 \)[/tex]
The correct choice is:
(D) [tex]\( x > -3 \)[/tex]
Given inequality:
[tex]\[ 3(-x + 2) < 15 \][/tex]
1. Distribute the 3 inside the parentheses:
[tex]\[ 3 \cdot -x + 3 \cdot 2 < 15 \][/tex]
[tex]\[ -3x + 6 < 15 \][/tex]
2. Subtract 6 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ -3x + 6 - 6 < 15 - 6 \][/tex]
[tex]\[ -3x < 9 \][/tex]
3. Divide both sides by -3 to solve for [tex]\( x \)[/tex]. Since we are dividing by a negative number, the inequality sign will flip:
[tex]\[ x > \frac{9}{-3} \][/tex]
[tex]\[ x > -3 \][/tex]
Therefore, the solution to the inequality is:
[tex]\[ \boxed{x > -3} \][/tex]
Comparing this to the choices given:
(A) [tex]\( x > 7 \)[/tex]
(B) [tex]\( x < 3 \)[/tex]
(C) [tex]\( x < -7 \)[/tex]
(D) [tex]\( x > -3 \)[/tex]
The correct choice is:
(D) [tex]\( x > -3 \)[/tex]
