How do you solve #78> 4x + 6#?

2 Answers
Mar 10, 2018

See a solution process belowL

Explanation:

First, subtract #color(red)(6)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#78 - color(red)(6) > 4x + 6 - color(red)(6)#

#72 > 4x + 0#

#72 > 4x#

Now, divide each side of the inequality by #color(red)(4)# to solve for #x# while keeping the inequality balanced:

#72/color(red)(4) > (4x)/color(red)(4)#

#18 > (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))#

#18 > x#

We can reverse or "flip" the entire inequality to state the solution in terms of #x#:

#x < 18#

Mar 10, 2018

#x<18#

Explanation:

For now, we can treat the inequality sign like an equal sign. We perform the normal operations as if this were #78=4x+6#.

We start by subtracting #6# from both sides to get:

#72>4x#

We can switch the sides if we like:

#4x<72#

And we can divide both sides by #4# to get:

#x<18# or #18>x#

*NOTE: The direction of the inequality does not change since I did not multiply or divide it by a negative. I only flipped the sign because the convention is usually to have the variable on the left.