Solve the compound inequality. Write the solution in interval notation.
-$12 x - 8

Question

Solve the compound inequality. Write the solution in interval notation.
-$12 x - 8 < 4 x \text { or } - 4 x \leq - 12$
A) $\varnothing$  
B)[1, 3]
C)(-?, 1)  $\cup$ [3, ?)
D)(1, 3)

Quizplus · Accepted Answer

First, solve each inequality separately. For $12x - 8 < 4x$, subtract $4x$ from both sides to get $8x - 8 < 0$, then add 8 to both sides to get $8x < 8$, and finally divide by 8 to get $x < 1$. For $-4x \leq -12$, divide both sides by -4 (remember to flip the inequality sign when dividing by a negative) to get $x \geq 3$. The solution is the union of these two inequalities, which is $x < 1$ or $x \geq 3$, represented in interval notation as $(-∞, 1) \cup [3, ∞)$.

Solve the Compound Inequality 12x−8<4x or −4x≤−1212 x - 8 < 4 x \text { or } - 4 x \leq - 1212x−8<4x or −4x≤−12

Solve the Compound Inequality $12 x - 8 < 4 x \text { or } - 4 x \leq - 12$