Which of the following values are solutions to the inequality -8 > 6x+8? I. 4 II. 6 III. -10 None I only II only III only I and II I and III II and III I, II and III

Isolate x in inequality: First, we need to isolate x in the inequality -8 > 6x + 8. Subtract 8 from both sides of the inequality to get: -8 - 8 > 6x + 8 - 8 -16 > 6x Now, divide both sides by 6 to solve for x: -16 / 6 > 6x / 6 -8/3 > x This simplifies to x < -8/3.Convert -8/3 to decimal: Now we need to check which of the given values are less than -8/3. First, we convert -8/3 to a decimal for easier comparison: -8/3 ≈ -2.67Check value I: Check if value I (4) is a solution: 4 6x + 8. So, the correct choice is ＂III only＂.

Home

Math Problems

Grade 8

Solutions to inequalities

Full solution

Q. Which of the following values are solutions to the inequality

-8>6 x+8 ?

\newline

4

\newline

II.

6

\newline

III.

-10

\newline

None

\newline

I only

\newline

II only

\newline

III only

\newline

I and II

\newline

I and III

\newline

II and III

\newline

I, II and III

Isolate x in inequality: First, we need to isolate x in the inequality -8 > 6x + 8. $\newline$ Subtract $8$ from both sides of the inequality to get: $\newline$ -8 - 8 > 6x + 8 - 8 $\newline$ -16 > 6x $\newline$ Now, divide both sides by $6$ to solve for x: $\newline$ -\frac{16}{6} > \frac{6x}{6} $\newline$ -\frac{8}{3} > x $\newline$ This simplifies to x < -\frac{8}{3}.
Convert $-\frac{8}{3}$ to decimal: Now we need to check which of the given values are less than $-\frac{8}{3}$ . $\newline$ First, we convert $-\frac{8}{3}$ to a decimal for easier comparison: $\newline$ $-\frac{8}{3} \approx -2.67$
Check value $I$ : Check if value $I (4)$ is a solution: $\newline$ 4 < -2.67 is false. $\newline$ So, $I (4)$ is not a solution.
Check value II: Check if value II $6$ is a solution: $\newline$ 6 < -2.67 is false. $\newline$ So, II $6$ is not a solution.
Check value III: Check if value III ( $-10$ ) is a solution: $\newline$ -10 < -2.67 is true. $\newline$ So, III ( $-10$ ) is a solution.
Identify solution: Based on the checks, only value III ( $-10$ ) is a solution to the inequality -8 > 6x + 8. So, the correct choice is ＂III only＂.