How do you solve #2(x-1) + 3= x -3(x+1)#?

Question

Nathan Axel · Accepted Answer

#x = -1#

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

First, use the distributive property to simplify #2(x-1)# and #-3(x+1)#:

Following this image, we know that:
#color(blue)(2(x-1) = (2 * x) + (2 * -1) = 2x - 1)#
and
#color(blue)(-3(x+1) = (-3 * x) + (-3 * 1) = -3x + -3)#

Put them back into the equation:
#2x - 2 + 3 = x - 3x - 3#

Simplify:
#2x + 1 = -2x - 3#

Add #color(blue)(2x)# to both sides of the equation:
#2x + 1 quadcolor(blue)(+quad2x) = -2x - 3 quadcolor(blue)(+quad2x)#

#4x + 1 = -3#

Subtract #color(blue)1# from both sides of the equation:
#4x + 1 quadcolor(blue)(-quad1) = -3 quadcolor(blue)(-quad1)#

#4x = -4#

Divide both sides by #color(blue)4#:
#(4x)/color(blue)4 = -4/color(blue)4#

Therefore,
#x = -1#

Hope this helps!

Eli Assouline · Answer

undefined To solve the equation 2(x-1) + 3 = x - 3(x+1), you would first distribute the terms inside the parentheses and then combine like terms.

Starting with the left side of the equation:
2(x-1) + 3 = 2x - 2 + 3 = 2x + 1

Now, for the right side of the equation:
x - 3(x+1) = x - 3x - 3 = -2x - 3

Now, equating the left and right sides of the equation:
2x + 1 = -2x - 3

Next, move all terms involving x to one side and constants to the other:
2x + 2x = -3 - 1
4x = -4

Now, divide both sides by 4:
x = -1