Solve Linear Inequalities
Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
-$$\frac { x - 3 } { 8 } \geq \frac { x - 2 } { 12 } + \frac { 1 } { 24 }$$

A) $[ 6 , \infty )$
B) $( - \infty , 6 ]$
C) $( 6 , \infty )$
D) $( - \infty , 6 )$ Use interval notation to represent all values of x satisfying the given conditions.

Question

Solve Linear Inequalities
Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
-$$\frac { x - 3 } { 8 } \geq \frac { x - 2 } { 12 } + \frac { 1 } { 24 }$$

A) $[ 6 , \infty )$ 
B) $( - \infty , 6 ]$ 
C) $( 6 , \infty )$ 
D) $( - \infty , 6 )$ Use interval notation to represent all values of x satisfying the given conditions.

Quizplus · Accepted Answer

First, we simplify the inequality:

$\frac { x - 3 } { 8 } \geq \frac { x - 2 } { 12 } + \frac { 1 } { 24 }$

$\frac { x - 3 } { 8 } \geq \frac { x + 1 } { 24 }$

$3(x - 3) \geq 2(x + 1)$ (multiplied both sides by 24 to eliminate the denominators)

$x \geq 6$

Therefore, the solution set is $[6, \infty)$.

Graph:

The closed circle at 6 indicates that 6 is included in the solution set, and the arrow to the right indicates that all values greater than 6 are also included in the solution set.

(Note: the graph may not be to scale)

So, the best choice is A.

Solve Linear Inequalities Solve the Linear Inequality x−38≥x−212+124\frac { x - 3 } { 8 } \geq \frac { x - 2 } { 12 } + \frac { 1 } { 24 }8x−3​≥12x−2​+241​

Solve Linear Inequalities
Solve the Linear Inequality $\frac { x - 3 } { 8 } \geq \frac { x - 2 } { 12 } + \frac { 1 } { 24 }$