Question 740097
EXPLANATION OF THE INEQUALITY SET-UP:
(Understand the explanation, but do not include in your homework, unless you are sure the teacher wants to see all of it)
{{{x}}}= the number
{{{x+6}}}= the sum of the number and 6
{{{4*(x+6)}}}= four times the sum of the number and 6
 
{{{6x}}}= 6 times the number
{{{6x-14}}}= 6 times the number less 14
 
{{{4*(x+6)}}} is at least {{{6x-14}}} means that
{{{4*(x+6)}}} is equal to or greater than {{{6x-14}}}
We write that as
{{{4*(x+6)>=6x-14}}}
 
THE SOLUTION:
{{{4*(x+6)>=6x-14}}}
{{{4x+24>=6x-14}}} (after applying the distributive property on the left side)
{{{24>=6x-4x-14}}} (after subtracting 4x from both sides)
{{{24+14>=6x-4x}}} (after adding 14 to both sides)
{{{38>=2x}}} (after performing indicated)
Then dividing both sides by 2, you get:
{{{19>=x}}} or {{{highlight(x<=19)}}}
(You may want to show less steps and explanations in the solution, according to what the teacher expects from you)