Question

solve $-6x + 3 \geq 21$. \
\
\bigcirc a. $x \leq 3$ \
\
\bigcirc b. $x \geq 3$ \
\
\bigcirc c. $x \geq -3$ \
\
\bigcirc d. $x \leq -3$

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the inequality \( -6x + 3 \geq 21 \). This gives us:
\( -6x + 3 - 3 \geq 21 - 3 \)
Simplifying both sides, we get:
\( -6x \geq 18 \)

Step2: Divide by -6 and reverse inequality

When we divide both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. So, we divide both sides of \( -6x \geq 18 \) by -6:
\( \frac{-6x}{-6} \leq \frac{18}{-6} \)
Simplifying both sides, we find:
\( x \leq -3 \)

Answer:

D. \( x \leq -3 \)