Solve the compound inequality. Write the solution in interval notation.
-$0 \leq \frac { 2 x + 1 } { 2 }

Question

Solve the compound inequality. Write the solution in interval notation.
-$0 \leq \frac { 2 x + 1 } { 2 } < 3$
A) $\left( - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$
B) $\left[ - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$.
C) $\left( - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)$
D) $\left[ - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$

Quizplus · Accepted Answer

To solve the compound inequality $0 \leq \frac { 2 x + 1 } { 2 } < 3$, we first multiply all parts by 2 to get rid of the denominator: $0 \leq 2x + 1 < 6$. Then, we subtract 1 from all parts: $-1 \leq 2x < 5$. Dividing by 2 gives $-\frac{1}{2} \leq x < \frac{5}{2}$. This translates to the interval notation $\left[ - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)$, but since both the original options B and D are identical and correctly represent the solution, the correct choice based on the provided options is B.

Solve the Compound Inequality 0≤2x+12<30 \leq \frac { 2 x + 1 } { 2 } < 30≤22x+1​<3

Solve the Compound Inequality $0 \leq \frac { 2 x + 1 } { 2 } < 3$