Solve (1,22+2,7x)*2-(1,5x-0,525):7,5=11,01+1,5(1,1x-3,3)

$$( 1,22 + 2,7 x ) \cdot 2 - ( 1,5 x - 0,525 ) : 7,5 = 11,01 + 1,5 ( 1,1 x - 3,3 )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1,22+2,7x by 2.

$$2,44+5,4x-\frac{1,5x-0,525}{7,5}=11,01+1,5\left(1,1x-3,3\right)$$

Use the distributive property to multiply 1,5 by 1,1x-3,3.

$$2,44+5,4x-\frac{1,5x-0,525}{7,5}=11,01+1,65x-4,95$$

Subtract 4,95 from 11,01 to get 6,06.

$$2,44+5,4x-\frac{1,5x-0,525}{7,5}=6,06+1,65x$$

Divide each term of 1,5x-0,525 by 7,5 to get \frac{1,5x}{7,5}+\frac{-0,525}{7,5}.

$$2,44+5,4x-\left(\frac{1,5x}{7,5}+\frac{-0,525}{7,5}\right)=6,06+1,65x$$

Divide 1,5x by 7,5 to get 0,2x.

$$2,44+5,4x-\left(0,2x+\frac{-0,525}{7,5}\right)=6,06+1,65x$$

Expand \frac{-0,525}{7,5} by multiplying both numerator and the denominator by 1000.

$$2,44+5,4x-\left(0,2x+\frac{-525}{7500}\right)=6,06+1,65x$$

Reduce the fraction \frac{-525}{7500} to lowest terms by extracting and canceling out 75.

$$2,44+5,4x-\left(0,2x-\frac{7}{100}\right)=6,06+1,65x$$

To find the opposite of 0,2x-\frac{7}{100}, find the opposite of each term.

$$2,44+5,4x-0,2x-\left(-\frac{7}{100}\right)=6,06+1,65x$$

The opposite of -\frac{7}{100} is \frac{7}{100}.

$$2,44+5,4x-0,2x+\frac{7}{100}=6,06+1,65x$$

Combine 5,4x and -0,2x to get 5,2x.

$$2,44+5,2x+\frac{7}{100}=6,06+1,65x$$

Convert decimal number 2,44 to fraction \frac{244}{100}. Reduce the fraction \frac{244}{100} to lowest terms by extracting and canceling out 4.

$$\frac{61}{25}+5,2x+\frac{7}{100}=6,06+1,65x$$

Least common multiple of 25 and 100 is 100. Convert \frac{61}{25} and \frac{7}{100} to fractions with denominator 100.

$$\frac{244}{100}+5,2x+\frac{7}{100}=6,06+1,65x$$

Since \frac{244}{100} and \frac{7}{100} have the same denominator, add them by adding their numerators.

$$\frac{244+7}{100}+5,2x=6,06+1,65x$$

Add 244 and 7 to get 251.

$$\frac{251}{100}+5,2x=6,06+1,65x$$

Subtract 1,65x from both sides.

$$\frac{251}{100}+5,2x-1,65x=6,06$$

Combine 5,2x and -1,65x to get 3,55x.

$$\frac{251}{100}+3,55x=6,06$$

Subtract \frac{251}{100} from both sides.

$$3,55x=6,06-\frac{251}{100}$$

Convert decimal number 6,06 to fraction \frac{606}{100}. Reduce the fraction \frac{606}{100} to lowest terms by extracting and canceling out 2.

$$3,55x=\frac{303}{50}-\frac{251}{100}$$

Least common multiple of 50 and 100 is 100. Convert \frac{303}{50} and \frac{251}{100} to fractions with denominator 100.

$$3,55x=\frac{606}{100}-\frac{251}{100}$$

Since \frac{606}{100} and \frac{251}{100} have the same denominator, subtract them by subtracting their numerators.

$$3,55x=\frac{606-251}{100}$$

Subtract 251 from 606 to get 355.

$$3,55x=\frac{355}{100}$$

Reduce the fraction \frac{355}{100} to lowest terms by extracting and canceling out 5.

$$3,55x=\frac{71}{20}$$

Divide both sides by 3,55.

$$x=\frac{\frac{71}{20}}{3,55}$$

Divide \frac{71}{20} by 3,55 to get 1.

$$x=1$$