6(r-7)+1=7(r+3)-28

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Solution for 6(r-7)+1=7(r+3)-28 equation:


Simplifying
6(r + -7) + 1 = 7(r + 3) + -28

Reorder the terms:
6(-7 + r) + 1 = 7(r + 3) + -28
(-7 * 6 + r * 6) + 1 = 7(r + 3) + -28
(-42 + 6r) + 1 = 7(r + 3) + -28

Reorder the terms:
-42 + 1 + 6r = 7(r + 3) + -28

Combine like terms: -42 + 1 = -41
-41 + 6r = 7(r + 3) + -28

Reorder the terms:
-41 + 6r = 7(3 + r) + -28
-41 + 6r = (3 * 7 + r * 7) + -28
-41 + 6r = (21 + 7r) + -28

Reorder the terms:
-41 + 6r = 21 + -28 + 7r

Combine like terms: 21 + -28 = -7
-41 + 6r = -7 + 7r

Solving
-41 + 6r = -7 + 7r

Solving for variable 'r'.

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

Add '-7r' to each side of the equation.
-41 + 6r + -7r = -7 + 7r + -7r

Combine like terms: 6r + -7r = -1r
-41 + -1r = -7 + 7r + -7r

Combine like terms: 7r + -7r = 0
-41 + -1r = -7 + 0
-41 + -1r = -7

Add '41' to each side of the equation.
-41 + 41 + -1r = -7 + 41

Combine like terms: -41 + 41 = 0
0 + -1r = -7 + 41
-1r = -7 + 41

Combine like terms: -7 + 41 = 34
-1r = 34

Divide each side by '-1'.
r = -34

Simplifying
r = -34

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