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How do you solve #4( 4x + 3) - 12= 5- 6( 5x + 2)#?

Answer 1

Ethan Adkins

#x = -7/46#

First, use the distributive property to simplify #color(blue)(4(4x+3))# and #color(blue)(-6(5x+2))#:

Following this image, we know that:
#color(blue)(4(4x+3) = (4 * 4x) + (4 * 3) = 16x + 12)#

and

#color(blue)(-6(5x+2) = (-6*5x) - (6 * 2) = -30x - 12)#

Now let's put them back into the equation:
#16x + 12 - 12 = 5 - 30x - 12#

Simplify:
#16x = -7 - 30x#

Add #color(blue)(30x)# to both sides of the equation:
#16x quadcolor(blue)(+quad30x) = -7 - 30x quadcolor(blue)(+quad30x)#

#46x = -7#

Divide both sides by #color(blue)46#:
#(46x)/color(blue)46 = -7/color(blue)46#

Therefore,
#x = -7/46#

Hope this helps!

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Answer 2

Eli Assouline

To solve the equation (4(4x + 3) - 12 = 5 - 6(5x + 2)), follow these steps:

Distribute the terms inside the parentheses: (16x + 12 - 12 = 5 - 30x - 12)
Combine like terms: (16x = 5 - 30x)
Add (30x) to both sides: (16x + 30x = 5)
Combine like terms: (46x = 5)
Divide both sides by (46): (x = \frac{5}{46})

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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.