Answer :
To solve the inequality [tex]\( 2(x - 4) + 14 \leq x - 1 \)[/tex], we need to follow these steps:
1. Expand and simplify the inequality:
[tex]\[ 2(x - 4) + 14 \leq x - 1 \][/tex]
First, distribute the 2 on the left-hand side:
[tex]\[ 2x - 8 + 14 \leq x - 1 \][/tex]
Simplify the terms inside the inequality:
[tex]\[ 2x + 6 \leq x - 1 \][/tex]
2. Isolate the variable [tex]\( x \)[/tex] on one side:
Subtract [tex]\( x \)[/tex] from both sides to get:
[tex]\[ 2x + 6 - x \leq x - 1 - x \][/tex]
Simplifying this:
[tex]\[ x + 6 \leq -1 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 6 from both sides:
[tex]\[ x + 6 - 6 \leq -1 - 6 \][/tex]
Simplify this to:
[tex]\[ x \leq -7 \][/tex]
Therefore, the solution to the inequality [tex]\( 2(x - 4) + 14 \leq x - 1 \)[/tex] is [tex]\( x \leq -7 \)[/tex].
From the given options:
A. [tex]\( x > -7 \)[/tex]
B. [tex]\( x \leq -7 \)[/tex]
C. [tex]\( -3 \leq x \leq 1 \)[/tex]
D. [tex]\( 1 < x < 4 \)[/tex]
The correct answer is B. [tex]\( x \leq -7 \)[/tex].
1. Expand and simplify the inequality:
[tex]\[ 2(x - 4) + 14 \leq x - 1 \][/tex]
First, distribute the 2 on the left-hand side:
[tex]\[ 2x - 8 + 14 \leq x - 1 \][/tex]
Simplify the terms inside the inequality:
[tex]\[ 2x + 6 \leq x - 1 \][/tex]
2. Isolate the variable [tex]\( x \)[/tex] on one side:
Subtract [tex]\( x \)[/tex] from both sides to get:
[tex]\[ 2x + 6 - x \leq x - 1 - x \][/tex]
Simplifying this:
[tex]\[ x + 6 \leq -1 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 6 from both sides:
[tex]\[ x + 6 - 6 \leq -1 - 6 \][/tex]
Simplify this to:
[tex]\[ x \leq -7 \][/tex]
Therefore, the solution to the inequality [tex]\( 2(x - 4) + 14 \leq x - 1 \)[/tex] is [tex]\( x \leq -7 \)[/tex].
From the given options:
A. [tex]\( x > -7 \)[/tex]
B. [tex]\( x \leq -7 \)[/tex]
C. [tex]\( -3 \leq x \leq 1 \)[/tex]
D. [tex]\( 1 < x < 4 \)[/tex]
The correct answer is B. [tex]\( x \leq -7 \)[/tex].
