Solve for z 1/2z+2(3/4z-1)=1/4z+6

Math
12z+2(34z-1)=14z+6
Simplify 12z+2(34z-1).
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Simplify each term.
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Combine 12 and z.
z2+2(34z-1)=14z+6
Combine 34 and z.
z2+2(3z4-1)=14z+6
Apply the distributive property.
z2+23z4+2⋅-1=14z+6
Cancel the common factor of 2.
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Factor 2 out of 4.
z2+23z2(2)+2⋅-1=14z+6
Cancel the common factor.
z2+23z2⋅2+2⋅-1=14z+6
Rewrite the expression.
z2+3z2+2⋅-1=14z+6
z2+3z2+2⋅-1=14z+6
Multiply 2 by -1.
z2+3z2-2=14z+6
z2+3z2-2=14z+6
Simplify terms.
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Combine fractions with similar denominators.
-2+z+3z2=14z+6
Add z and 3z.
-2+4z2=14z+6
Reduce the expression 4z2 by cancelling the common factors.
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Factor 2 out of 4z.
-2+2(2z)2=14z+6
Factor 2 out of 2.
-2+2(2z)2(1)=14z+6
Cancel the common factor.
-2+2(2z)2⋅1=14z+6
Rewrite the expression.
-2+2z1=14z+6
-2+2z1=14z+6
Divide 2z by 1.
-2+2z=14z+6
-2+2z=14z+6
-2+2z=14z+6
Combine 14 and z.
-2+2z=z4+6
Move all terms containing z to the left side of the equation.
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Subtract z4 from both sides of the equation.
-2+2z-z4=6
To write 2z as a fraction with a common denominator, multiply by 44.
-2+2z⋅44-z4=6
Combine 2z and 44.
-2+2z⋅44-z4=6
Combine the numerators over the common denominator.
-2+2z⋅4-z4=6
Simplify each term.
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Simplify the numerator.
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Factor z out of 2z⋅4-z.
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Factor z out of 2z⋅4.
-2+z(2⋅4)-z4=6
Factor z out of -z.
-2+z(2⋅4)+z⋅-14=6
Factor z out of z(2⋅4)+z⋅-1.
-2+z(2⋅4-1)4=6
-2+z(2⋅4-1)4=6
Multiply 2 by 4.
-2+z(8-1)4=6
Subtract 1 from 8.
-2+z⋅74=6
-2+z⋅74=6
Move 7 to the left of z.
-2+7z4=6
-2+7z4=6
-2+7z4=6
Move all terms not containing z to the right side of the equation.
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Add 2 to both sides of the equation.
7z4=6+2
Add 6 and 2.
7z4=8
7z4=8
Multiply both sides of the equation by 47.
47⋅7z4=47⋅8
Simplify both sides of the equation.
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Simplify 47⋅7z4.
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Cancel the common factor of 4.
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Cancel the common factor.
47⋅7z4=47⋅8
Rewrite the expression.
17⋅(7z)=47⋅8
17⋅(7z)=47⋅8
Cancel the common factor of 7.
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Factor 7 out of 7z.
17⋅(7(z))=47⋅8
Cancel the common factor.
17⋅(7z)=47⋅8
Rewrite the expression.
z=47⋅8
z=47⋅8
z=47⋅8
Multiply 47⋅8.
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Combine 47 and 8.
z=4⋅87
Multiply 4 by 8.
z=327
z=327
z=327
The result can be shown in multiple forms.
Exact Form:
z=327
Decimal Form:
z=4.571428‾
Mixed Number Form:
z=447
Solve for z 1/2z+2(3/4z-1)=1/4z+6

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