Solve the inequality and express the solution set using interval notation. $8 ( 7 - x ) \leq 10 ( 7 - x )$
A) $[ 8 , \infty )$
B) $( - \infty , 8 ]$
C) $[ 7 , \infty )$
D) $( - \infty , 7 ]$
E) $[ 7 , \infty ]$

Question

Quizplus · Accepted Answer

First, we can simplify the inequality by dividing both sides by 2: 
$$4(7-x) \leq 5(7-x)$$
Next, we can subtract $5(7-x)$ from both sides: 
$$-1(7-x) \leq 0$$
This is equivalent to $$x-7 \geq 0$$
which means $$x\geq 7$$
Therefore, the solution set is $$(- \infty, 7]$$ which corresponds to choice D.

Solve the Inequality and Express the Solution Set Using Interval 8(7−x)≤10(7−x)8 ( 7 - x ) \leq 10 ( 7 - x )8(7−x)≤10(7−x)

Solve the Inequality and Express the Solution Set Using Interval $8 ( 7 - x ) \leq 10 ( 7 - x )$