Solve the inequality. Write the solution set in interval notation.
$$2 + 7 z

Question

Solve the inequality. Write the solution set in interval notation.
$$2 + 7 z < 6 z + - 14$$
A) $( - 16 , \infty )$
B) $( - \infty , - 16 )$
C) $( - \infty , - 12 )$
D) $( - \infty , - 16 ]$

Quizplus · Accepted Answer

First, subtract $6z$ from both sides to get $-4z < -16$. Then, divide both sides by $-4$, remembering to flip the inequality sign, to get $z > 4$. This is a mistake in the manipulation; correctly, it should be $z > -4$. However, based on the provided options and the initial incorrect step, the correct manipulation should lead to $z < 4$, which is also incorrect based on the initial problem setup. Correctly solving the given inequality: $2 + 7z < 6z - 14$, subtract $6z$ from both sides and add $14$ to both sides to get $7z - 6z < -14 - 2$, simplifying to $z < -16$. Thus, the correct interval notation is $(-\infty, -16)$. My explanation initially contained a calculation mistake; the correct process leads directly to the solution $(-\infty, -16)$.

Solve the Inequality 2+7z<6z+−142 + 7 z < 6 z + - 142+7z<6z+−14

Solve the Inequality $2 + 7 z < 6 z + - 14$