How do you solve #3x+1=1/2#?

Question

Julia Adams · Accepted Answer

#x=-1/6#

Subtract #1# from both sides

#3x+1-1=1/2-1#

#3x=-1/2#

And then divide both sides by #3#

#(3x)/3=(-1/2)/3#

#-1/2# divided by #3# can also be written as #-1/2# multiplied by #1/3#

#x=(-1/2)*1/3#

#x=-1/6#

Alternatively put,* *

Bring #1# to the other side, making sure to change its sign

#3x=1/2-1#

#3x=-1/2#

And divide both numerators by #3#

#(3x)/3=-1/(2*3)#

#x=-1/6#

Eva Adamson · Answer

#x = -1/6#

In order to solve this, we need to "balance the equation." First, let's take the true equation 5 = 5, which we can write as (5) = (5). The brackets simply indicate what the original "elements" of the equation were as a group. Next, let's take the false statement (5) -1 = 5, which we can balance by writing (5) -1 = (5) - 1. We have used the same procedure on both sides.

Solving the original equation using the same idea: The target is to get #x# on one side of the equals sign and everything else on the other.

First isolate all the elements with #x# in them. That is "#3x#"

#(3x+1)=(1/2)#

Step1. Subtract 1 from both sides giving: #(3x+1) -1=(1/2)-1# #3x=-1/2#

Step2. Now we need to separate the 3 from the #x# and move it to the other side of the equals sign. This is done by changing 3 into #1# as #1 times x = x#. Dividing by three is the same as multiply by #1/3#.

Split each side in half.

#(3x) times 1/3 = (-1/2) times 1/3#

#3/3 times x = (-1 times 1)/(2 times 3)#

thus #x = -1/6#

Eva Abramson · Answer

undefined To solve the equation 3x + 1 = 1/2, you would first subtract 1 from both sides to isolate the term with the variable. This gives you 3x = 1/2 - 1. Next, you would simplify the right side to obtain 3x = -1/2. Finally, you would divide both sides by 3 to solve for x, resulting in x = -1/6.