3a+1=4a-6

Solution for 3a+1=4a-6 equation:

Simplifying
3a + 1 = 4a + -6

Reorder the terms:
1 + 3a = 4a + -6

Reorder the terms:
1 + 3a = -6 + 4a

Solving
1 + 3a = -6 + 4a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-4a' to each side of the equation.
1 + 3a + -4a = -6 + 4a + -4a

Combine like terms: 3a + -4a = -1a
1 + -1a = -6 + 4a + -4a

Combine like terms: 4a + -4a = 0
1 + -1a = -6 + 0
1 + -1a = -6

Add '-1' to each side of the equation.
1 + -1 + -1a = -6 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = -6 + -1
-1a = -6 + -1

Combine like terms: -6 + -1 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7