Answer :
To solve the inequality [tex]\(16x + 8 \geq 12x + 20\)[/tex], let's go through the steps systematically.
1. Isolate the terms involving [tex]\(x\)[/tex]:
We start by moving the terms involving [tex]\(x\)[/tex] to one side of the inequality. This involves subtracting [tex]\(12x\)[/tex] from both sides:
[tex]\[ 16x + 8 \geq 12x + 20 \][/tex]
Subtract [tex]\(12x\)[/tex] from both sides:
[tex]\[ 16x - 12x + 8 \geq 20 \][/tex]
2. Simplify the inequality:
Combine like terms on the left side:
[tex]\[ 4x + 8 \geq 20 \][/tex]
3. Isolate the constant term:
Next, we want to isolate [tex]\(4x\)[/tex] by moving the constant term on the left side to the right side of the inequality. This involves subtracting 8 from both sides:
[tex]\[ 4x + 8 - 8 \geq 20 - 8 \][/tex]
Simplify:
[tex]\[ 4x \geq 12 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, we solve for [tex]\(x\)[/tex] by dividing both sides of the inequality by 4:
[tex]\[ \frac{4x}{4} \geq \frac{12}{4} \][/tex]
Simplify:
[tex]\[ x \geq 3 \][/tex]
Thus, the solution to the inequality [tex]\(16x + 8 \geq 12x + 20\)[/tex] is [tex]\( x \geq 3 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x \geq 3 \)[/tex]
1. Isolate the terms involving [tex]\(x\)[/tex]:
We start by moving the terms involving [tex]\(x\)[/tex] to one side of the inequality. This involves subtracting [tex]\(12x\)[/tex] from both sides:
[tex]\[ 16x + 8 \geq 12x + 20 \][/tex]
Subtract [tex]\(12x\)[/tex] from both sides:
[tex]\[ 16x - 12x + 8 \geq 20 \][/tex]
2. Simplify the inequality:
Combine like terms on the left side:
[tex]\[ 4x + 8 \geq 20 \][/tex]
3. Isolate the constant term:
Next, we want to isolate [tex]\(4x\)[/tex] by moving the constant term on the left side to the right side of the inequality. This involves subtracting 8 from both sides:
[tex]\[ 4x + 8 - 8 \geq 20 - 8 \][/tex]
Simplify:
[tex]\[ 4x \geq 12 \][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, we solve for [tex]\(x\)[/tex] by dividing both sides of the inequality by 4:
[tex]\[ \frac{4x}{4} \geq \frac{12}{4} \][/tex]
Simplify:
[tex]\[ x \geq 3 \][/tex]
Thus, the solution to the inequality [tex]\(16x + 8 \geq 12x + 20\)[/tex] is [tex]\( x \geq 3 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x \geq 3 \)[/tex]
