How do you solve #2(x-4)<=2+3(x-6)#?

Answer 1

Eva Abramson

#x>=8#

The first step is to distribute the brackets on both sides of the inequality.

#rArr2x-8<=2+3x-18#

Next, collect terms in x to one side and numeric values on the other side.

subtract 2x from both sides.

#cancel(2x)cancel(-2x)-8<=2+3x-2x-18#

#rArr-8<=x-16#

Isolate x on the right side by adding 16 to both sides.

#-8+16<=xcancel(-16)cancel(+16)#

#rArr8<=xrArrx>=8#

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Answer 2

Eva Abramson

To solve the inequality 2(x-4) ≤ 2 + 3(x-6), you would first distribute the coefficients:

2x - 8 ≤ 2 + 3x - 18

Then, combine like terms:

2x - 8 ≤ 3x - 16

Next, subtract 2x from both sides:

-8 ≤ x - 16

Finally, add 16 to both sides:

8 ≤ x

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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.

How do you solve #2(x-4)&lt;=2+3(x-6)#?

How do you solve #2(x-4)<=2+3(x-6)#?