To solve the inequality [tex]\( 20x + 12 \geq 14x + 30 \)[/tex], we'll follow these steps:
1. Start with the original inequality:
[tex]\[ 20x + 12 \geq 14x + 30 \][/tex]
2. Isolate the variables on one side of the inequality.
Subtract [tex]\( 14x \)[/tex] from both sides:
[tex]\[ 20x - 14x + 12 \geq 14x - 14x + 30 \][/tex]
Simplifies to:
[tex]\[ 6x + 12 \geq 30 \][/tex]
3. Isolate the constant term on the other side of the inequality.
Subtract 12 from both sides:
[tex]\[ 6x + 12 - 12 \geq 30 - 12 \][/tex]
Simplifies to:
[tex]\[ 6x \geq 18 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by the coefficient of [tex]\( x \)[/tex]:
[tex]\[ \frac{6x}{6} \geq \frac{18}{6} \][/tex]
Simplifies to:
[tex]\[ x \geq 3 \][/tex]
So, the solution to the inequality [tex]\( 20x + 12 \geq 14x + 30 \)[/tex] is:
[tex]\[ x \geq 3 \][/tex]
The correct answer is:
C. [tex]\( x \geq 3 \)[/tex]
