How do you solve #2x/3+9=-7#?

2 Answers

Answer:

Use the formula PESADM
#x = -24#

Explanation:

In solving for an unknown always work backwards.
First remove any Parenthesis and Exponents

# x/3# is actually a parenthesis #(x/3)#

To remove the parenthesis multiply everything by 3. This gives

# cancel3 xx 2(x/cancel3) + 3 xx 9 = 3 xx -7# The result is

#2x + 27 = - 21 #

Now that the PE is taken care of do SA (subtraction and addition)

Subtract 27 or add - 27 to both sides This gives

#2x + 27 - 27 = -21 -27" "# The result is

(subtracting from a negative gives more negatives)
A negative goes down, adding another negative goes further down. So the answer is very down
Think " I fell into a burning ring of fire I went down down down and the flame went higher and it burns burns burns the ring of fire".

#2x = - 48#

The PE and the SA are taken care of now do the DM

Divide both sides by #2" "# This gives

#(2x)/2 = -48/2 " "# The result is

#x = -24# ( a negative divided by a positive is a negative)

PESADM Think if you find you lost your cell phone in PE you are a SAD M(am)

Oct 19, 2016

Answer:

It is not clear what is intended in the first term? #2 x/3#
There are two possible solutions.
#x = -54 " or " x = -24#

Explanation:

It is not clear what is intended in the first term? #2 x/3#

Is this to be regarded as a mixed fraction, which is generally not used in algebra?

There is nothing to indicate that is is a multiplication?

One of #" "2(x/3) " "2*x/3 " " 2xx x/3# would have been clearer

Let's look at both possibilities.

Option 1

Write #2 x/3 # as an improper fraction, giving #(6+x)/3#

#(6+x)/3 +9color(red)(-9) = -7color(red)(-9)" "larr# add -9 to both sides

#(color(blue)(3xx)(6+x))/3 = -16color(blue)(xx3)color(white)(xxxxxxxxx)larr xx 3# on both sides

#6+x = -48" "larr # subtract 6 from both sides

#x = -48-6#

#x = -54#

Option 2

#2(x/3) +9color(red)(-9) = -7color(red)(-9)" "larr# subtract 9 from each side

#(color(blue)(3xx)2x)/3 = -16color(blue)(xx3)color(white)(xxxxxxxxx)larr xx 3# on both sides

#2x = -48#

#x = -24#