Solve for h (8h-7)/3+(4(2h-5))/6-1=(7h-4)/2

Math
8h-73+4(2h-5)6-1=7h-42
Move 7h-42 to the left side of the equation by subtracting it from both sides.
8h-73+4(2h-5)6-1-7h-42=0
Simplify 8h-73+4(2h-5)6-1-7h-42.
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Simplify terms.
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Cancel the common factor of 4 and 6.
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Factor 2 out of 4(2h-5).
8h-73+2(2(2h-5))6-1-7h-42=0
Cancel the common factors.
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Factor 2 out of 6.
8h-73+2(2(2h-5))2(3)-1-7h-42=0
Cancel the common factor.
8h-73+2(2(2h-5))2⋅3-1-7h-42=0
Rewrite the expression.
8h-73+2(2h-5)3-1-7h-42=0
8h-73+2(2h-5)3-1-7h-42=0
8h-73+2(2h-5)3-1-7h-42=0
Combine the numerators over the common denominator.
8h-7+2(2h-5)3-1-7h-42=0
8h-7+2(2h-5)3-1-7h-42=0
Simplify the numerator.
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Apply the distributive property.
8h-7+2(2h)+2⋅-53-1-7h-42=0
Multiply 2 by 2.
8h-7+4h+2⋅-53-1-7h-42=0
Multiply 2 by -5.
8h-7+4h-103-1-7h-42=0
Add 8h and 4h.
12h-7-103-1-7h-42=0
Subtract 10 from -7.
12h-173-1-7h-42=0
12h-173-1-7h-42=0
To write -1 as a fraction with a common denominator, multiply by 33.
12h-173-1⋅33-7h-42=0
Combine -1 and 33.
12h-173+-1⋅33-7h-42=0
Combine the numerators over the common denominator.
12h-17-1⋅33-7h-42=0
Simplify the expression.
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Multiply -1 by 3.
12h-17-33-7h-42=0
Subtract 3 from -17.
12h-203-7h-42=0
12h-203-7h-42=0
Factor 4 out of 12h-20.
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Factor 4 out of 12h.
4(3h)-203-7h-42=0
Factor 4 out of -20.
4(3h)+4(-5)3-7h-42=0
Factor 4 out of 4(3h)+4(-5).
4(3h-5)3-7h-42=0
4(3h-5)3-7h-42=0
To write 4(3h-5)3 as a fraction with a common denominator, multiply by 22.
4(3h-5)3⋅22-7h-42=0
To write -7h-42 as a fraction with a common denominator, multiply by 33.
4(3h-5)3⋅22-7h-42⋅33=0
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
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Multiply 4(3h-5)3 and 22.
4(3h-5)⋅23⋅2-7h-42⋅33=0
Multiply 3 by 2.
4(3h-5)⋅26-7h-42⋅33=0
Multiply 7h-42 and 33.
4(3h-5)⋅26-(7h-4)⋅32⋅3=0
Multiply 2 by 3.
4(3h-5)⋅26-(7h-4)⋅36=0
4(3h-5)⋅26-(7h-4)⋅36=0
Combine the numerators over the common denominator.
4(3h-5)⋅2-(7h-4)⋅36=0
Simplify the numerator.
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Apply the distributive property.
(4(3h)+4⋅-5)⋅2-(7h-4)⋅36=0
Multiply 3 by 4.
(12h+4⋅-5)⋅2-(7h-4)⋅36=0
Multiply 4 by -5.
(12h-20)⋅2-(7h-4)⋅36=0
Apply the distributive property.
12h⋅2-20⋅2-(7h-4)⋅36=0
Multiply 2 by 12.
24h-20⋅2-(7h-4)⋅36=0
Multiply -20 by 2.
24h-40-(7h-4)⋅36=0
Apply the distributive property.
24h-40+(-(7h)–4)⋅36=0
Multiply 7 by -1.
24h-40+(-7h–4)⋅36=0
Multiply -1 by -4.
24h-40+(-7h+4)⋅36=0
Apply the distributive property.
24h-40-7h⋅3+4⋅36=0
Multiply 3 by -7.
24h-40-21h+4⋅36=0
Multiply 4 by 3.
24h-40-21h+126=0
Subtract 21h from 24h.
3h-40+126=0
Add -40 and 12.
3h-286=0
3h-286=0
Reduce the expression by cancelling the common factors.
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Split the fraction into multiple fractions.
3h6-286=0
Reduce the expression 3h6 by cancelling the common factors.
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Factor 3 out of 3h.
3(h)6-286=0
Factor 3 out of 6.
3h3⋅2-286=0
Cancel the common factor.
3h3⋅2-286=0
Rewrite the expression.
h2-286=0
h2-286=0
Reduce the expression 286 by cancelling the common factors.
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Factor 2 out of 28.
h2-2(14)6=0
Factor 2 out of 6.
h2-2⋅142⋅3=0
Cancel the common factor.
h2-2⋅142⋅3=0
Rewrite the expression.
h2-143=0
h2-143=0
h2-143=0
h2-143=0
Find the LCD of the terms in the equation.
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To find the LCD of a set of numbers (h2,-143), find the LCM of the denominators.
LCM(2,3)
Calculate the LCM of first two denominators in the list, 2 and 3.
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Find the values of the numerical part of each term. Select the largest one, which in this case is 3. Multiply them together to get the current total. In this case, the current total is 6.
Current Total = 6
Multiply the numeric part of the denominators together.
Current Total = 3+3=6
Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.
6
6
6
Multiply each term by 6 and simplify.
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Multiply each term in h2-143=0 by 6.
h2⋅6-143⋅6=0⋅6
Simplify each term.
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Cancel the common factor of 2.
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Factor 2 out of 6.
h2⋅(2(3))-143⋅6=0⋅6
Cancel the common factor.
h2⋅(2⋅3)-143⋅6=0⋅6
Rewrite the expression.
h⋅3-143⋅6=0⋅6
h⋅3-143⋅6=0⋅6
Move 3 to the left of h.
3⋅h-143⋅6=0⋅6
Cancel the common factor of 3.
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Move the leading negative in -143 into the numerator.
3h+-143⋅6=0⋅6
Factor 3 out of 6.
3h+-143⋅(3(2))=0⋅6
Cancel the common factor.
3h+-143⋅(3⋅2)=0⋅6
Rewrite the expression.
3h-14⋅2=0⋅6
3h-14⋅2=0⋅6
Multiply -14 by 2.
3h-28=0⋅6
3h-28=0⋅6
Multiply 0 by 6.
3h-28=0
3h-28=0
Add 28 to both sides of the equation.
3h=28
Divide each term by 3 and simplify.
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Divide each term in 3h=28 by 3.
3h3=283
Cancel the common factor of 3.
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Cancel the common factor.
3h3=283
Divide h by 1.
h=283
h=283
h=283
The result can be shown in multiple forms.
Exact Form:
h=283
Decimal Form:
h=9.3‾
Mixed Number Form:
h=913
Solve for h (8h-7)/3+(4(2h-5))/6-1=(7h-4)/2

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