Solve the inequality. Write the solution set in interval notation.
-$$- 1 - 2 ( 2 x + 1 )

Question

Solve the inequality. Write the solution set in interval notation.
-$$- 1 - 2 ( 2 x + 1 ) < x - ( - 1 - x )$$
A) $\left( - \infty , - \frac { 2 } { 3 } \right]$
B) $\left[ - \frac { 2 } { 3 } , \infty \right)$
C) $\left( - \frac { 2 } { 3 } , \infty \right)$
D) $( - \infty , - 1 )$

Quizplus · Accepted Answer

First, simplify the inequality: $$-1 - 2(2x + 1) < x - (-1 - x)$$ becomes $$-1 - 4x - 2 < x + 1 + x$$, which simplifies to $$-3 - 4x < 2x + 1$$. Adding 4x to both sides and adding 3 to both sides gives $$0 < 6x + 4$$, which simplifies to $$0 < 6x + 4$$. Dividing by 6 gives $$0 < x + \frac{2}{3}$$, leading to $$x > -\frac{2}{3}$$. Therefore, the solution in interval notation is $\left( - \frac { 2 } { 3 } , \infty \right)$.

Solve the Inequality −1−2(2x+1)<x−(−1−x)- 1 - 2 ( 2 x + 1 ) < x - ( - 1 - x )−1−2(2x+1)<x−(−1−x)

Solve the Inequality $- 1 - 2 ( 2 x + 1 ) < x - ( - 1 - x )$