Question

What would 3g + 5 < -2 look like on a number line?

a) G is a point to the right of -1.
b) G is a point to the left of -1.
c) G is a point to the right of 1.
d) G is a point to the left of 1.

Answer 1

The inequality 3g + 5 < -2 when solved for g shows that g is any value less than -7/3, which means on a number line, g is to the left of -1. Thus, the correct answer is b. G is a point to the left of -1.

Step-by-step explanation:

When analyzing the inequality 3g + 5 < -2, our first step is to isolate the variable g on one side. We start by subtracting 5 from both sides of the inequality:

3g + 5 - 5 < -2 - 5

3g < -7

Next, we divide both sides by 3 to solve for g:

3g / 3 < -7 / 3

g < -7/3

Since -7/3 is roughly -2.33, on a number line, g would be any point to the left of -2.33. Therefore, option b, which states 'G is a point to the left of -1,' is incorrect since g is actually to the left of -2.33, and -2.33 is less than -1. The correct answer is b. G is a point to the left of -1, considering that on a number line, any number smaller than -1 lies to the left of it.