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How do you solve #a-2<3a+2(a+3)#?

Answer 1

Kennedy Adams

#a > -2#

Given: #color(white)("XXX")a-2 < 2a+2(a+3)#

Simplify the right side: #color(white)("XXX")a-2 < 3a +2a+6#

#color(white)("XXX")a-2 < 5a+6#

Subtract #(a+6)# from both sides #color(white)("XXX")-8 < 4a#

Divide both sides by #4# #color(white)("XXX")-2 < acolor(white)("XX")orcolor(white)("XX")a > -2#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Remember: When working with inequalities you can: #color(white)("XXX")#add or subtract the same amount to both sides; and #color(white)("XXX")#multiply or divide both sides by the same positive amount. without changing the direction of the inequality sign.

If you multiply or divide both sides by an negative amount: #color(white)("XXX")#the inequality sign must be reversed.

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Answer 2

Hazel Anglin

To solve the inequality ( a - 2 < 3a + 2(a + 3) ), follow these steps:

Distribute the ( 2 ) on the right side: ( a - 2 < 3a + 2a + 6 )
Combine like terms: ( a - 2 < 5a + 6 )
Subtract ( a ) from both sides: ( -2 < 4a + 6 )
Subtract ( 6 ) from both sides: ( -8 < 4a )
Divide both sides by ( 4 ): ( -2 < a )

So, the solution is ( a > -2 ).

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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 #a-2&lt;3a+2(a+3)#?

How do you solve #a-2<3a+2(a+3)#?