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How do you solve the inequality #3-4(x-2) >=-5x+6#?

Answer 1

Abigail Allen

#x >= -5#

#3-4(x-2) >= -5x + 6#

Simplify the left hand side: #3 - 4x + 8 >= -5x + 6#

#11 - 4x >= -5x + 6#

Add #color(blue)(5x)# to both sides: #11 - 4x quadcolor(blue)(+quad5x) >= -5x + 6 quadcolor(blue)(+quad5x)#

#11 + x >= 6#

Subtract #color(blue)11# from both sides: #11 + x quadcolor(blue)(-quad11) > 6 quadcolor(blue)(-quad11)#

#x >= -5#

Hope this helps!

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Answer 2

Eva Adamson

To solve the inequality 3 - 4(x - 2) ≥ -5x + 6, follow these steps:

Distribute the -4 across the parentheses: 3 - 4x + 8 ≥ -5x + 6.
Combine like terms: -4x + 11 ≥ -5x + 6.
Add 5x to both sides to isolate the variable terms: x + 11 ≥ 6.
Subtract 11 from both sides: x ≥ -5.

The solution to the inequality is x ≥ -5.

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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 the inequality #3-4(x-2) &gt;=-5x+6#?

How do you solve the inequality #3-4(x-2) >=-5x+6#?