Solve the following linear equations.
-2x+3=-x-2
Consider the equation:
-2x+3=-x-2
Add 2x to both sides:
-2x+3+2x=-x-2+2x
3=x-2
Add 2 to both sides:
3+2=x-2+2
5=x
The solution is x=5.
2x-1=-x+5
Consider the equation:
2x-1=-x+5
Add x to both sides:
2x -1 + x = -x+5 + x
3x-1=5
Add 1 to both sides:
3x-1+1=5+1
3x=6
Divide both sides by 3.
\dfrac{3x}{3}=\dfrac{6}{3}
x=2
The solution is x=2.
-3x-3=x+-5
Consider the equation:
-3x-3 = x +5
Add 3x to both sides:
-3x-3 + 3x = x + 5 + 3x
-3 = 4x+5
Subtract 5 from both sides:
-3 -5 = 4x+5 - 5
-8=4x
Divide both sides by 4.
\dfrac{-8}{4}=\dfrac{4x}{4}
x=-2
The solution is x=-2
-x-3=3x+1
Consider the equation:
-x-3=3x+1
Add x to both sides:
-x-3+x = 3x + 1+x
-3 = 4x+1
Subtract 1 from both sides:
-3 -1= 4x + 1-1
-4 = 4x
Divide both sides by 4.
\dfrac{-4}{4}=\dfrac{4x}{4}
x=-1
The solution is x=-1
-x + 5 = -2x-3
Consider the equation:
-x + 5 = -2x-3
Add x to both sides:
-x + 5 +x= -2x-3+x
5=-x-3
Add 3 to both sides:
5+3 = -x-3+3
8=-x
Divide both sides by -1.
\dfrac {8} {-1} = \dfrac {-x} {-1}
x = -8
The solution is x=-8.
5x-2=-4x+7
Consider the equation:
5x-2=-4x+7
Add 4x to both sides:
5x-2 +4x= -4x+7+4x
9x-2=7
Add 2 to both sides:
9x-2+2 = 7+2
9x=9
Divide both sides by 9.
\dfrac {9x} {9} = \dfrac {9} {9}
x = 1
The solution is x=1.
9-2x=3x-11
Consider the equation:
9-2x=3x-11
Add 2x to both sides:
9-2x+2x = 3x-11+2x
9=5x-11
Add 11 to both sides:
9+11 = 5x-11+11
5x=20
Divide both sides by 5.
\dfrac {5x} {5} = \dfrac {20} {5}
x = 4
The solution is x=4.