Question

if $2x + 6 < 12$, what is the solution for $x$?
a. $x < 3$
b. $x < 9$
c. $x > 9$
d. $x > 3$

what does the inequality $x \geq 5$ represent?
a. $x$ is less than or equal to 5
b. $x$ is greater than or equal to 5
c. $x$ is greater than 5
d. $x$ is less than 5

Explanation:

Step1: Subtract 6 from both sides

\(2x + 6 - 6 < 12 - 6\)
\(2x < 6\)

Step2: Divide both sides by 2

\(\frac{2x}{2} < \frac{6}{2}\)
\(x < 3\)

The inequality \(x \geq 5\) uses the symbol "≥", which means "greater than or equal to". So it represents that \(x\) takes values that are either greater than 5 or exactly equal to 5.

Answer:

a. \(x < 3\)
b. b. \(x\) is greater than or equal to 5