Solve for t 1/2*(4t-7)=(t+7)/4

Math
12⋅(4t-7)=t+74
Move t+74 to the left side of the equation by subtracting it from both sides.
12⋅(4t-7)-t+74=0
Simplify 12⋅(4t-7)-t+74.
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Simplify each term.
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Apply the distributive property.
12(4t)+12⋅-7-t+74=0
Cancel the common factor of 2.
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Factor 2 out of 4t.
12(2(2t))+12⋅-7-t+74=0
Cancel the common factor.
12(2(2t))+12⋅-7-t+74=0
Rewrite the expression.
2t+12⋅-7-t+74=0
2t+12⋅-7-t+74=0
Combine 12 and -7.
2t+-72-t+74=0
Move the negative in front of the fraction.
2t-72-t+74=0
2t-72-t+74=0
To write 2t as a fraction with a common denominator, multiply by 44.
2t⋅44-t+74-72=0
Simplify terms.
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Combine 2t and 44.
2t⋅44-t+74-72=0
Combine the numerators over the common denominator.
2t⋅4-(t+7)4-72=0
2t⋅4-(t+7)4-72=0
Simplify the numerator.
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Multiply 4 by 2.
8t-(t+7)4-72=0
Apply the distributive property.
8t-t-1⋅74-72=0
Multiply -1 by 7.
8t-t-74-72=0
Subtract t from 8t.
7t-74-72=0
Factor 7 out of 7t-7.
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Factor 7 out of 7t.
7(t)-74-72=0
Factor 7 out of -7.
7(t)+7(-1)4-72=0
Factor 7 out of 7(t)+7(-1).
7(t-1)4-72=0
7(t-1)4-72=0
7(t-1)4-72=0
To write -72 as a fraction with a common denominator, multiply by 22.
7(t-1)4-72⋅22=0
Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.
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Multiply 72 and 22.
7(t-1)4-7⋅22⋅2=0
Multiply 2 by 2.
7(t-1)4-7⋅24=0
7(t-1)4-7⋅24=0
Combine the numerators over the common denominator.
7(t-1)-7⋅24=0
Simplify the numerator.
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Factor 7 out of 7(t-1)-7⋅2.
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Factor 7 out of -7⋅2.
7(t-1)+7(-1⋅2)4=0
Factor 7 out of 7(t-1)+7(-1⋅2).
7(t-1-1⋅2)4=0
7(t-1-1⋅2)4=0
Multiply -1 by 2.
7(t-1-2)4=0
Subtract 2 from -1.
7(t-3)4=0
7(t-3)4=0
7(t-3)4=0
Since this is the only denominator in the list, the result is the LCD: 4.
4
Multiply each term by 4 and simplify.
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Multiply each term in 7(t-3)4=0 by 4.
7(t-3)4⋅4=0⋅4
Simplify 7(t-3)4⋅4.
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Cancel the common factor of 4.
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Cancel the common factor.
7(t-3)4⋅4=0⋅4
Rewrite the expression.
7(t-3)=0⋅4
7(t-3)=0⋅4
Apply the distributive property.
7t+7⋅-3=0⋅4
Multiply 7 by -3.
7t-21=0⋅4
7t-21=0⋅4
Multiply 0 by 4.
7t-21=0
7t-21=0
Add 21 to both sides of the equation.
7t=21
Divide each term by 7 and simplify.
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Divide each term in 7t=21 by 7.
7t7=217
Cancel the common factor of 7.
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Cancel the common factor.
7t7=217
Divide t by 1.
t=217
t=217
Divide 21 by 7.
t=3
t=3
Solve for t 1/2*(4t-7)=(t+7)/4

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