Solve the inequality. Use algebra to solve the corresponding equation.
-$$\mathrm { x } ^ { 2 } + 2 \mathrm { x } \geq 3$$
A) $[ 1 , \infty )$
B) $[ - 3,1 ]$
C) $( - \infty , - 3 ] \cup [ 1 , \infty )$
D) $( - \infty , - 3 ]$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to get $\mathrm { x } ^ { 2 } + 2 \mathrm { x } - 3 \geq 0$. Factoring the quadratic gives $(x + 3)(x - 1) \geq 0$. The roots are $x = -3$ and $x = 1$. Testing intervals around these roots shows that the inequality holds for $x \leq -3$ and $x \geq 1$, leading to the solution set $( - \infty , - 3 ] \cup [ 1 , \infty )$.

Solve the Inequality x2+2x≥3\mathrm { x } ^ { 2 } + 2 \mathrm { x } \geq 3x2+2x≥3

Solve the Inequality $\mathrm { x } ^ { 2 } + 2 \mathrm { x } \geq 3$