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10. Solve the following inequality: [tex]2(x+1) - (-x+5) \leq -18[/tex].

A. [tex]x \leq -37[/tex]
B. [tex]x \leq -5[/tex]
C. [tex]x \leq -9[/tex]
D. [tex]x \leq -20[/tex]


Sagot :

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].