5(r-2)=2(r-3)-7

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Solution for 5(r-2)=2(r-3)-7 equation:


Simplifying
5(r + -2) = 2(r + -3) + -7

Reorder the terms:
5(-2 + r) = 2(r + -3) + -7
(-2 * 5 + r * 5) = 2(r + -3) + -7
(-10 + 5r) = 2(r + -3) + -7

Reorder the terms:
-10 + 5r = 2(-3 + r) + -7
-10 + 5r = (-3 * 2 + r * 2) + -7
-10 + 5r = (-6 + 2r) + -7

Reorder the terms:
-10 + 5r = -6 + -7 + 2r

Combine like terms: -6 + -7 = -13
-10 + 5r = -13 + 2r

Solving
-10 + 5r = -13 + 2r

Solving for variable 'r'.

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

Add '-2r' to each side of the equation.
-10 + 5r + -2r = -13 + 2r + -2r

Combine like terms: 5r + -2r = 3r
-10 + 3r = -13 + 2r + -2r

Combine like terms: 2r + -2r = 0
-10 + 3r = -13 + 0
-10 + 3r = -13

Add '10' to each side of the equation.
-10 + 10 + 3r = -13 + 10

Combine like terms: -10 + 10 = 0
0 + 3r = -13 + 10
3r = -13 + 10

Combine like terms: -13 + 10 = -3
3r = -3

Divide each side by '3'.
r = -1

Simplifying
r = -1

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