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How do you solve # -x / 7 + 4 ≥ 3x#?

Answer 1

Ethan Adkins

#x <= 14/11 " or " x <= 1 3/11#

Given: #-x/7 + 4 >= 3x#

The easiest way to start is to get rid of the fraction by multiplying the whole inequality by #7#:

#-x/cancel(7) *cancel(7)/1+ 4*7 >= 3x*7#

#-x+ 28 >= 21x#

Add #x# to both sides: #" "28 >= 22x#

Divide by #22#: #" "28/22 >= x#

Reduce the fraction: #" "14/11 >= x#

This means #x <= 14/11 " or " x <= 1 3/11#

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Answer 2

Isaiah Anthony

#x<=14/11#

To get rid of the #7# in the denominator, we can multiply all terms by #7#. This leaves us with

#-x+28>=21x#

Since we did the same thing to both sides, we did not inadvertently change the meaning of this equation.

What we can do next is add #x# to both sides. We get

#22x<=28#

Dividing both sides by #22# gives us

#x<=28/22#

which can be simplified as

#x<=14/11#

Hope this helps!

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Answer 3

Genesis Allen

To solve the inequality -x/7 + 4 ≥ 3x, we can follow these steps:

Get rid of the fraction by multiplying all terms by 7 to clear the denominator: 7(-x/7) + 7(4) ≥ 7(3x) -x + 28 ≥ 21x
Simplify the equation: -x + 28 ≥ 21x 28 ≥ 22x
Divide by 22 to isolate x: 28/22 ≥ x 14/11 ≥ x

So, the solution to the inequality is x ≤ 14/11 or in decimal form, x ≤ 1.27.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.