Answer :
To solve the inequality [tex]\( 2(x + 1) - (-x + 5) \leq -18 \)[/tex], let's go through the steps in detail.
1. Expand and simplify the inequality:
Start with the given inequality:
[tex]\[ 2(x + 1) - (-x + 5) \leq -18 \][/tex]
Distribute the terms inside the parentheses:
[tex]\[ 2x + 2 - (-x + 5) \leq -18 \][/tex]
Simplify the negative signs:
[tex]\[ 2x + 2 + x - 5 \leq -18 \][/tex]
Combine like terms:
[tex]\[ 3x - 3 \leq -18 \][/tex]
2. Isolate the variable:
Add 3 to both sides of the inequality:
[tex]\[ 3x - 3 + 3 \leq -18 + 3 \][/tex]
Simplify:
[tex]\[ 3x \leq -15 \][/tex]
Divide both sides by 3:
[tex]\[ x \leq -5 \][/tex]
3. Conclusion:
The solution to the inequality [tex]\( 2(x + 1) - (-x + 5) \leq -18 \)[/tex] is:
[tex]\[ x \leq -5 \][/tex]
Therefore, the correct answer is:
B. [tex]\( x \leq -5 \)[/tex].
1. Expand and simplify the inequality:
Start with the given inequality:
[tex]\[ 2(x + 1) - (-x + 5) \leq -18 \][/tex]
Distribute the terms inside the parentheses:
[tex]\[ 2x + 2 - (-x + 5) \leq -18 \][/tex]
Simplify the negative signs:
[tex]\[ 2x + 2 + x - 5 \leq -18 \][/tex]
Combine like terms:
[tex]\[ 3x - 3 \leq -18 \][/tex]
2. Isolate the variable:
Add 3 to both sides of the inequality:
[tex]\[ 3x - 3 + 3 \leq -18 + 3 \][/tex]
Simplify:
[tex]\[ 3x \leq -15 \][/tex]
Divide both sides by 3:
[tex]\[ x \leq -5 \][/tex]
3. Conclusion:
The solution to the inequality [tex]\( 2(x + 1) - (-x + 5) \leq -18 \)[/tex] is:
[tex]\[ x \leq -5 \][/tex]
Therefore, the correct answer is:
B. [tex]\( x \leq -5 \)[/tex].
