Solve x+6x-3/4+15x-9/2+20x-45/4+15x-15+6x-45/4+x-frac{9}{2}-frac{3}{4}=16

$$x+6x- \frac{ 3 }{ 4 } +15x- \frac{ 9 }{ 2 } +20x- \frac{ 45 }{ 4 } +15x-15+6x- \frac{ 45 }{ 4 } +x- \frac{ 9 }{ 2 } - \frac{ 3 }{ 4 } =16$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Combine x and 6x to get 7x.

$$7x-\frac{3}{4}+15x-\frac{9}{2}+20x-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Combine 7x and 15x to get 22x.

$$22x-\frac{3}{4}-\frac{9}{2}+20x-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{9}{2} to fractions with denominator 4.

$$22x-\frac{3}{4}-\frac{18}{4}+20x-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Since -\frac{3}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$22x+\frac{-3-18}{4}+20x-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Subtract 18 from -3 to get -21.

$$22x-\frac{21}{4}+20x-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Combine 22x and 20x to get 42x.

$$42x-\frac{21}{4}-\frac{45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Since -\frac{21}{4} and \frac{45}{4} have the same denominator, subtract them by subtracting their numerators.

$$42x+\frac{-21-45}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Subtract 45 from -21 to get -66.

$$42x+\frac{-66}{4}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Reduce the fraction \frac{-66}{4} to lowest terms by extracting and canceling out 2.

$$42x-\frac{33}{2}+15x-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Combine 42x and 15x to get 57x.

$$57x-\frac{33}{2}-15+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Convert 15 to fraction \frac{30}{2}.

$$57x-\frac{33}{2}-\frac{30}{2}+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Since -\frac{33}{2} and \frac{30}{2} have the same denominator, subtract them by subtracting their numerators.

$$57x+\frac{-33-30}{2}+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Subtract 30 from -33 to get -63.

$$57x-\frac{63}{2}+6x-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Combine 57x and 6x to get 63x.

$$63x-\frac{63}{2}-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Least common multiple of 2 and 4 is 4. Convert -\frac{63}{2} and \frac{45}{4} to fractions with denominator 4.

$$63x-\frac{126}{4}-\frac{45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Since -\frac{126}{4} and \frac{45}{4} have the same denominator, subtract them by subtracting their numerators.

$$63x+\frac{-126-45}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Subtract 45 from -126 to get -171.

$$63x-\frac{171}{4}+x-\frac{9}{2}-\frac{3}{4}=16$$

Combine 63x and x to get 64x.

$$64x-\frac{171}{4}-\frac{9}{2}-\frac{3}{4}=16$$

Least common multiple of 4 and 2 is 4. Convert -\frac{171}{4} and \frac{9}{2} to fractions with denominator 4.

$$64x-\frac{171}{4}-\frac{18}{4}-\frac{3}{4}=16$$

Since -\frac{171}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$64x+\frac{-171-18}{4}-\frac{3}{4}=16$$

Subtract 18 from -171 to get -189.

$$64x-\frac{189}{4}-\frac{3}{4}=16$$

Since -\frac{189}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$64x+\frac{-189-3}{4}=16$$

Subtract 3 from -189 to get -192.

$$64x+\frac{-192}{4}=16$$

Divide -192 by 4 to get -48.

$$64x-48=16$$

Add 48 to both sides.

$$64x=16+48$$

Add 16 and 48 to get 64.

$$64x=64$$

Divide both sides by 64.

$$x=\frac{64}{64}$$

Divide 64 by 64 to get 1.

$$x=1$$