How do you solve #3- 2( x + 6) = - 1( x - 1) + 7#?

Question

Isaiah Anthony · Accepted Answer

#x=-17#

#"distribute parenthesis on both sides of the equation"#

#3-2x-12=-x+1+7larrcolor(blue)"collect like terms"#

#rArr-2x-9=-x+8#

#"add 2x to both sides"#

#cancel(-2x)cancel(+2x)-9=2x-x+8#

#rArr-9=x+8#

#"subtract 8 from both sides"#

#-9-8=xcancel(+8)cancel(-8)#

#rArr-17=xrArrx=-17#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left "=3-(2xx-11)=3-(-22)=3+22=25#

#"right "=(-1xx-18)+7=18+7=25#

#rArrx=-17" is the solution"#

Eva Abramson · Answer

#x=-17# #3-2(x+6)=-1(x-1)+7# #3-2x-12=-x+1+7# #-2x-9=-x+8# #-9=x+8# #x=-9-8# #x=-17#

Kennedy Adams · Answer

undefined To solve the equation $3 - 2(x + 6) = -1(x - 1) + 7$, follow these steps:

1. Distribute the terms inside the parentheses:
   $3 - 2x - 12 = -x + 1 + 7$

2. Combine like terms on both sides of the equation:
   $3 - 12 - 2x = -x + 8$

3. Simplify:
   $-9 - 2x = -x + 8$

4. Add $x$ to both sides to isolate terms with $x$ on one side of the equation:
   $-9 - 2x + x = 8$

5. Simplify:
   $-9 - x = 8$

6. Add 9 to both sides:
   $-x = 17$

7. Multiply both sides by -1 to solve for $x$:
   $x = -17$