Question

-6x + 3 ≥ 15
options:
○ x ≤ -2
○ x ≥ -3
○ x ≥ -2
○ x ≤ -3

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the inequality \( -6x + 3 \geq 15 \). This gives us \( -6x + 3 - 3 \geq 15 - 3 \), which simplifies to \( -6x \geq 12 \).

Step2: Divide by -6 and reverse inequality

When dividing an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -6x \geq 12 \) by -6, we get \( \frac{-6x}{-6} \leq \frac{12}{-6} \), which simplifies to \( x \leq -2 \). Wait, no, wait. Wait, \( 15 - 3 = 12 \), then \( -6x \geq 12 \), dividing both sides by -6 (and reversing the inequality) gives \( x \leq -2 \)? Wait, no, let's check again. Wait, the original inequality is \( -6x + 3 \geq 15 \). Subtract 3: \( -6x \geq 12 \). Divide by -6: \( x \leq -2 \)? But wait, the options have \( x \leq -2 \) as one of them? Wait, no, the options are: first option (leftmost) is \( x \leq -2 \), then \( x \geq -3 \), \( x \geq -2 \), \( x \leq -3 \). Wait, maybe I made a mistake. Wait, let's re - do the calculation.

Wait, \( -6x+3\geq15 \)

Subtract 3: \( -6x\geq15 - 3=12 \)

Divide both sides by - 6: when dividing by a negative number, the inequality sign flips. So \( x\leq\frac{12}{-6}=-2 \)

So the solution is \( x\leq - 2 \)

Wait, but let's check the options. The left - most option (after Clear All) is \( x\leq - 2 \)? Wait, the options are:

1. \( x\leq - 2 \)

1. \( x\geq - 3 \)

1. \( x\geq - 2 \)

1. \( x\leq - 3 \)

So the correct one is the first option (the left - most radio button) with \( x\leq - 2 \)? Wait, no, wait the user's image: the options are (from left to right after Clear All):

1. \( x\leq - 2 \)

1. \( x\geq - 3 \)

1. \( x\geq - 2 \)

1. \( x\leq - 3 \)

Wait, but let's re - solve the inequality:

\( -6x + 3\geq15 \)

Subtract 3: \( -6x\geq12 \)

Divide by - 6: \( x\leq - 2 \) (because dividing by a negative number reverses the inequality)

So the correct option is the first one (the left - most) with \( x\leq - 2 \)

Wait, but maybe I misread the options. Let's check again. The user's image: the options are:

• First option: \( x\leq - 2 \)

• Second: \( x\geq - 3 \)

• Third: \( x\geq - 2 \)

• Fourth: \( x\leq - 3 \)

So the solution to \( -6x + 3\geq15 \) is \( x\leq - 2 \), which is the first option.

Answer:

The correct option is the left - most radio button with \( x\leq - 2 \) (i.e., the option labeled \( x\leq - 2 \))