Use algebraic and/or graphical methods to solve the inequality.
- $( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$

Question

Use algebraic and/or graphical methods to solve the inequality.
-$$( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$$
A) $x < - \frac { 7 } { 2 }$ or $\frac { 7 } { 3 } < x < 8$
B) $- \frac { 7 } { 2 } \leq x \leq \frac { 7 } { 3 }$ or $x \geq 8$
C) $- \frac { 7 } { 2 } < x < \frac { 7 } { 3 }$ or $x > 8$
D) $x \leq - \frac { 7 } { 2 }$ or $\frac { 7 } { 3 } \leq x \leq 8$

Quizplus · Accepted Answer

To solve the inequality $(2x + 7)(x - 8)(3x - 7) \leq 0$, we find the roots of the equation $(2x + 7)(x - 8)(3x - 7) = 0$, which are $x = -\frac{7}{2}$, $x = 8$, and $x = \frac{7}{3}$. Plotting these on a number line and testing intervals between and outside these points, we find that the inequality is satisfied for $x \leq -\frac{7}{2}$, $\frac{7}{3} \leq x \leq 8$.

Use Algebraic And/or Graphical Methods to Solve the Inequality (2x+7)(x−8)(3x−7)≤0( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0(2x+7)(x−8)(3x−7)≤0

Use Algebraic And/or Graphical Methods to Solve the Inequality $( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$