Question

Solve the following equation and find value of x:

$(x - 1) - (2x) = (3x + 2) - (x - 1)$
Please answer step by step. ​

Answer 1

Answer:

x - 1 - 2x = 3x + 2 - x + 1

3x + 2x - x - x = -1 - 3

3x = -4

x = -4/3

Answer 2

Answer:

$\displaystyle\left(x-1\right)-\left(2x\right)=\left(3x+2\right)-\left(x-1\right)\quad :\quad x=-\frac{4}{3}\quad \left(\mathrm{Decimal}:\quad x=-1.33333\dots \right)$

Step-by-step explanation:

$\left(x-1\right)-\left(2x\right)=\left(3x+2\right)-\left(x-1\right)$

$\gray{\mathrm{Remove\:parentheses}:\quad \left(a\right)=a}$

$x-1-2x=\left(3x+2\right)-\left(x-1\right)$

$\gray{\mathrm{Group\:like\:terms}}$

$x-2x-1=\left(3x+2\right)-\left(x-1\right)$

$\gray{\mathrm{Add\:similar\:elements:}\:x-2x=-x}$

$-x-1=3x+2-\left(x-1\right)$

$\gray{\mathrm{Expand\:}3x+2-\left(x-1\right):\quad 2x+3}$

$-x-1=2x+3$

$\gray{\mathrm{Add\:}1\mathrm{\:to\:both\:sides}}$

$-x-1+1=2x+3+1$

$\gray{\mathrm{Simplify}}$

$-x=2x+4$

$\gray{\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}}$

$-x-2x=2x+4-2x$

$\gray{\mathrm{Simplify}}$

$-3x=4$

$\gray{\mathrm{Divide\:both\:sides\:by\:}-3}$

$\displaystyle\frac{-3x}{-3}=\frac{4}{-3}$

$\gray{\mathrm{Simplify}}$

$\displaystyle x=-\frac{4}{3}$