Pls Help! Put a proper answer! And do not put a link or I will report you! Two times the sum of a number, x, and 9 is at most four times the number. Write and solve an inequality to find the value of the number.

9 ≤ x or x ≥ 9

Step-by-step explanation:

An inequality is like an equation, except instead of = they use <, >, ≤ or ≥.

Also like most equations you will see an inequality has two sides.  your problem seperates them with the term "is at most" so one side is "Two times the sum of a number, x, and 9" and the other is "four times the number"  So lets go part by part.

"Two times the sum of a number"  Two times the sum means something that looks like this 2(x+y) 2 is multiplying the sum of x + y.  It specifies the sum is x and 9 so it looks like 2(x+9)  That's one side.

four times the number is super easy, just 4x

so we have 2(x+9) is at most 4x

saying "is at most" is saying it can be less or equal to but not greater.  what symbol is less than or equal to?  ≤  so the full inequality looks like 2(x+9) ≤ 4x

Now, to solve you treat it like an equation.  if you multiply or divide both sides by a negative you flip the inequality symbol.  for instance -5x < 20 would turn into x > -4  Even if we don't use that here, it' super importnt to know.

Now lets solve the inequality.

2(x+9) ≤ 4x divide both sides by 2

x + 9 ≤ 2x Subtract x from both sides

9 ≤ x

So our number x must be 9 or more.  we cn try it out.

Plug n a number greater than 9 into 2(x+9) ≤ 4x.  I choose 10.  this gets us 38 ≤ 40, which shows 10 is a valid answer.  let's pick 9 itself.  this gets us 36 ≤ 36 which again is valid since ≤ is less than OR equal to.  if you pick a number less than 9 now it shouldn't work.  I choose 8.  This gets us 34 ≤32 which is not correct as expected.  

Thinking graphically 2(x+9) ≤ 4x is asking "when is the graph of 2(x+9)below or equal to 4x?"  if you graph 2(x+9) and 4x you will see that 2(x+9) is equalt o 4x when x equals 9, and then is below 4x after that.  all points before x = 9 2(x+9) is above 4x.

Let me know if there was anything you didn't understand.

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