Solve for x
x=5
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7\left(3x+7\right)+4\left(5x-4\right)=28x+14\left(3\times 2+1\right)
Multiply both sides of the equation by 28, the least common multiple of 4,7,2.
21x+49+4\left(5x-4\right)=28x+14\left(3\times 2+1\right)
Use the distributive property to multiply 7 by 3x+7.
21x+49+20x-16=28x+14\left(3\times 2+1\right)
Use the distributive property to multiply 4 by 5x-4.
41x+49-16=28x+14\left(3\times 2+1\right)
Combine 21x and 20x to get 41x.
41x+33=28x+14\left(3\times 2+1\right)
Subtract 16 from 49 to get 33.
41x+33=28x+14\left(6+1\right)
Multiply 3 and 2 to get 6.
41x+33=28x+14\times 7
Add 6 and 1 to get 7.
41x+33=28x+98
Multiply 14 and 7 to get 98.
41x+33-28x=98
Subtract 28x from both sides.
13x+33=98
Combine 41x and -28x to get 13x.
13x=98-33
Subtract 33 from both sides.
13x=65
Subtract 33 from 98 to get 65.
x=\frac{65}{13}
Divide both sides by 13.
x=5
Divide 65 by 13 to get 5.
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