# Solve for g (7g-21)/3-(2g-7)/4+1=5g-2

7g-213-2g-74+1=5g-2
Simplify 7g-213-2g-74+1.
Factor 7 out of 7g-21.
Factor 7 out of 7g.
7(g)-213-2g-74+1=5g-2
Factor 7 out of -21.
7g+7⋅-33-2g-74+1=5g-2
Factor 7 out of 7g+7⋅-3.
7(g-3)3-2g-74+1=5g-2
7(g-3)3-2g-74+1=5g-2
To write 7(g-3)3 as a fraction with a common denominator, multiply by 44.
7(g-3)3⋅44-2g-74+1=5g-2
To write -2g-74 as a fraction with a common denominator, multiply by 33.
7(g-3)3⋅44-2g-74⋅33+1=5g-2
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply 7(g-3)3 and 44.
7(g-3)⋅43⋅4-2g-74⋅33+1=5g-2
Multiply 3 by 4.
7(g-3)⋅412-2g-74⋅33+1=5g-2
Multiply 2g-74 and 33.
7(g-3)⋅412-(2g-7)⋅34⋅3+1=5g-2
Multiply 4 by 3.
7(g-3)⋅412-(2g-7)⋅312+1=5g-2
7(g-3)⋅412-(2g-7)⋅312+1=5g-2
Combine the numerators over the common denominator.
7(g-3)⋅4-(2g-7)⋅312+1=5g-2
Simplify each term.
Simplify the numerator.
Apply the distributive property.
(7g+7⋅-3)⋅4-(2g-7)⋅312+1=5g-2
Multiply 7 by -3.
(7g-21)⋅4-(2g-7)⋅312+1=5g-2
Apply the distributive property.
7g⋅4-21⋅4-(2g-7)⋅312+1=5g-2
Multiply 4 by 7.
28g-21⋅4-(2g-7)⋅312+1=5g-2
Multiply -21 by 4.
28g-84-(2g-7)⋅312+1=5g-2
Apply the distributive property.
28g-84+(-(2g)–7)⋅312+1=5g-2
Multiply 2 by -1.
28g-84+(-2g–7)⋅312+1=5g-2
Multiply -1 by -7.
28g-84+(-2g+7)⋅312+1=5g-2
Apply the distributive property.
28g-84-2g⋅3+7⋅312+1=5g-2
Multiply 3 by -2.
28g-84-6g+7⋅312+1=5g-2
Multiply 7 by 3.
28g-84-6g+2112+1=5g-2
Subtract 6g from 28g.
22g-84+2112+1=5g-2
22g-6312+1=5g-2
22g-6312+1=5g-2
Split the fraction into multiple fractions.
22g12-6312+1=5g-2
Reduce the expression 22g12 by cancelling the common factors.
Factor 2 out of 22g.
2(11g)12-6312+1=5g-2
Factor 2 out of 12.
2(11g)2(6)-6312+1=5g-2
Cancel the common factor.
2(11g)2⋅6-6312+1=5g-2
Rewrite the expression.
11g6-6312+1=5g-2
11g6-6312+1=5g-2
Reduce the expression 6312 by cancelling the common factors.
Factor 3 out of 63.
11g6-3(21)12+1=5g-2
Factor 3 out of 12.
11g6-3⋅213⋅4+1=5g-2
Cancel the common factor.
11g6-3⋅213⋅4+1=5g-2
Rewrite the expression.
11g6-214+1=5g-2
11g6-214+1=5g-2
11g6-214+1=5g-2
11g6-214+1=5g-2
Simplify 11g6-214+1.
Write 1 as a fraction with a common denominator.
11g6-214+44=5g-2
Combine the numerators over the common denominator.
11g6+-21+44=5g-2
11g6+-174=5g-2
Move the negative in front of the fraction.
11g6-174=5g-2
11g6-174=5g-2
Move all terms containing g to the left side of the equation.
Subtract 5g from both sides of the equation.
11g6-174-5g=-2
To write -5g as a fraction with a common denominator, multiply by 66.
11g6-5g⋅66-174=-2
Combine -5g and 66.
11g6+-5g⋅66-174=-2
Combine the numerators over the common denominator.
11g-5g⋅66-174=-2
Simplify each term.
Simplify the numerator.
Factor g out of 11g-5g⋅6.
Factor g out of 11g.
g⋅11-5g⋅66-174=-2
Factor g out of -5g⋅6.
g⋅11+g(-5⋅6)6-174=-2
Factor g out of g⋅11+g(-5⋅6).
g(11-5⋅6)6-174=-2
g(11-5⋅6)6-174=-2
Multiply -5 by 6.
g(11-30)6-174=-2
Subtract 30 from 11.
g⋅-196-174=-2
g⋅-196-174=-2
Move -19 to the left of g.
-19⋅g6-174=-2
Move the negative in front of the fraction.
-19g6-174=-2
-19g6-174=-2
-19g6-174=-2
Move all terms not containing g to the right side of the equation.
Add 174 to both sides of the equation.
-19g6=-2+174
To write -2 as a fraction with a common denominator, multiply by 44.
-19g6=-2⋅44+174
Combine -2 and 44.
-19g6=-2⋅44+174
Combine the numerators over the common denominator.
-19g6=-2⋅4+174
Simplify the numerator.
Multiply -2 by 4.
-19g6=-8+174
-19g6=94
-19g6=94
-19g6=94
Multiply both sides of the equation by -619.
-619⋅(-19g6)=-619⋅94
Simplify both sides of the equation.
Simplify -619⋅(-19g6).
Cancel the common factor of 6.
Move the leading negative in -619 into the numerator.
-619⋅(-19g6)=-619⋅94
Move the leading negative in -19g6 into the numerator.
-619⋅-19g6=-619⋅94
Factor 6 out of -6.
6(-1)19⋅-19g6=-619⋅94
Cancel the common factor.
6⋅-119⋅-19g6=-619⋅94
Rewrite the expression.
-119⋅(-19g)=-619⋅94
-119⋅(-19g)=-619⋅94
Cancel the common factor of 19.
Factor 19 out of -19g.
-119⋅(19(-g))=-619⋅94
Cancel the common factor.
-119⋅(19(-g))=-619⋅94
Rewrite the expression.
-1⋅(-g)=-619⋅94
-1⋅(-g)=-619⋅94
Multiply.
Multiply -1 by -1.
1⋅g=-619⋅94
Multiply g by 1.
g=-619⋅94
g=-619⋅94
g=-619⋅94
Simplify -619⋅94.
Cancel the common factor of 2.
Move the leading negative in -619 into the numerator.
g=-619⋅94
Factor 2 out of -6.
g=2(-3)19⋅94
Factor 2 out of 4.
g=2⋅-319⋅92⋅2
Cancel the common factor.
g=2⋅-319⋅92⋅2
Rewrite the expression.
g=-319⋅92
g=-319⋅92
Multiply -319 and 92.
g=-3⋅919⋅2
Simplify the expression.
Multiply -3 by 9.
g=-2719⋅2
Multiply 19 by 2.
g=-2738
Move the negative in front of the fraction.
g=-2738
g=-2738
g=-2738
g=-2738
The result can be shown in multiple forms.
Exact Form:
g=-2738
Decimal Form:
g=-0.71052631…
Solve for g (7g-21)/3-(2g-7)/4+1=5g-2

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