Negative three times a number plus four is no more than the number minus eight. What is the number?

2 Answers
Jun 28, 2018

Answer:

number #n# is such that #n>=3#

Explanation:

Let the number be #n#

Three times the number is #-3 xx n# = #3n#

Plus four is #-3n +4#

Number minus eight is #n - 8#

No more than is #<=#

So we get:

#-3n+4 <= n - 8#

Simplify and solve this linear equation:

#-3n-n <= -8-4#

#-4n <= -12#

#n >= -12/-4#

#n >= 3#

So the number #n# is such that #n>=3#

Hope this helps!

Jun 28, 2018

Answer:

See a solution process below:

Explanation:

"a number" #-> n#

"Negative three times a number" #-> -3n#

"Negative three times a number plus four" #-> -3n + 4#

"is no more than" #-> <=# giving:

#-3n <=#

"the number minus eight" #-> n - 8# giving:

#-3n + 4 <= n - 8#

Next, subtract #color(red)(n)# and #color(blue)(4)# from each side of the inequality to isolate the #n# term while keeping the inequality balanced:

#-3n - color(red)(n) + 4 - color(blue)(4) <= n - color(red)(n) - 8 - color(blue)(4)#

#-3n - color(red)(1n) + 0 <= 0 - 12#

#(-3 - color(red)(1))n <= -12#

#-4n <= -12#

Now, divide each side of the inequality by #color(blue)(-4)# to solve for #n# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator.

#(-4n)/color(blue)(-4) color(red)(>=) (-12)/color(blue)(-4)#

#(color(blue)(cancel(color(black)(-4)))n)/cancel(color(blue)(-4)) color(red)(>=) 3#

#n >= 3#