Solve (((93+87+5x)div7)*0.9+((100+90+5x)div7)*0.1)*0.6+0.1*95+0.3*97=97

$$(((93+87+5x) \div 7) \times 0.9+((100+90+5x) \div 7) \times 0.1) \times 0.6+0.1 \times 95+0.3 \times 97=97$$

Solve for x

$$x = \frac{1501}{15} = 100\frac{1}{15} \approx 100.066666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$7\left(\frac{93+87+5x}{7}\times 0.9+\frac{100+90+5x}{7}\times 0.1\right)\times 0.6+0.7\times 95+2.1\times 97=679$$

Add 93 and 87 to get 180.

$$7\left(\frac{180+5x}{7}\times 0.9+\frac{100+90+5x}{7}\times 0.1\right)\times 0.6+0.7\times 95+2.1\times 97=679$$

Add 100 and 90 to get 190.

$$7\left(\frac{180+5x}{7}\times 0.9+\frac{190+5x}{7}\times 0.1\right)\times 0.6+0.7\times 95+2.1\times 97=679$$

Multiply 7 and 0.6 to get 4.2.

$$4.2\left(\frac{180+5x}{7}\times 0.9+\frac{190+5x}{7}\times 0.1\right)+0.7\times 95+2.1\times 97=679$$

Use the distributive property to multiply 4.2 by \frac{180+5x}{7}\times 0.9+\frac{190+5x}{7}\times 0.1.

$$4.2\times \frac{180+5x}{7}\times 0.9+4.2\times \frac{190+5x}{7}\times 0.1+0.7\times 95+2.1\times 97=679$$

Multiply 4.2 and 0.9 to get 3.78.

$$3.78\times \frac{180+5x}{7}+4.2\times \frac{190+5x}{7}\times 0.1+0.7\times 95+2.1\times 97=679$$

Multiply 4.2 and 0.1 to get 0.42.

$$3.78\times \frac{180+5x}{7}+0.42\times \frac{190+5x}{7}+0.7\times 95+2.1\times 97=679$$

Multiply 0.7 and 95 to get 66.5.

$$3.78\times \frac{180+5x}{7}+0.42\times \frac{190+5x}{7}+66.5+2.1\times 97=679$$

Multiply 2.1 and 97 to get 203.7.

$$3.78\times \frac{180+5x}{7}+0.42\times \frac{190+5x}{7}+66.5+203.7=679$$

Add 66.5 and 203.7 to get 270.2.

$$3.78\times \frac{180+5x}{7}+0.42\times \frac{190+5x}{7}+270.2=679$$

Divide each term of 180+5x by 7 to get \frac{180}{7}+\frac{5}{7}x.

$$3.78\left(\frac{180}{7}+\frac{5}{7}x\right)+0.42\times \frac{190+5x}{7}+270.2=679$$

Use the distributive property to multiply 3.78 by \frac{180}{7}+\frac{5}{7}x.

$$3.78\times \frac{180}{7}+3.78\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Convert decimal number 3.78 to fraction \frac{378}{100}. Reduce the fraction \frac{378}{100} to lowest terms by extracting and canceling out 2.

$$\frac{189}{50}\times \frac{180}{7}+3.78\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Multiply \frac{189}{50} times \frac{180}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{189\times 180}{50\times 7}+3.78\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Do the multiplications in the fraction \frac{189\times 180}{50\times 7}.

$$\frac{34020}{350}+3.78\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Reduce the fraction \frac{34020}{350} to lowest terms by extracting and canceling out 70.

$$\frac{486}{5}+3.78\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Convert decimal number 3.78 to fraction \frac{378}{100}. Reduce the fraction \frac{378}{100} to lowest terms by extracting and canceling out 2.

$$\frac{486}{5}+\frac{189}{50}\times \frac{5}{7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Multiply \frac{189}{50} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{486}{5}+\frac{189\times 5}{50\times 7}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Do the multiplications in the fraction \frac{189\times 5}{50\times 7}.

$$\frac{486}{5}+\frac{945}{350}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Reduce the fraction \frac{945}{350} to lowest terms by extracting and canceling out 35.

$$\frac{486}{5}+\frac{27}{10}x+0.42\times \frac{190+5x}{7}+270.2=679$$

Divide each term of 190+5x by 7 to get \frac{190}{7}+\frac{5}{7}x.

$$\frac{486}{5}+\frac{27}{10}x+0.42\left(\frac{190}{7}+\frac{5}{7}x\right)+270.2=679$$

Use the distributive property to multiply 0.42 by \frac{190}{7}+\frac{5}{7}x.

$$\frac{486}{5}+\frac{27}{10}x+0.42\times \frac{190}{7}+0.42\times \frac{5}{7}x+270.2=679$$

Convert decimal number 0.42 to fraction \frac{42}{100}. Reduce the fraction \frac{42}{100} to lowest terms by extracting and canceling out 2.

$$\frac{486}{5}+\frac{27}{10}x+\frac{21}{50}\times \frac{190}{7}+0.42\times \frac{5}{7}x+270.2=679$$

Multiply \frac{21}{50} times \frac{190}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{486}{5}+\frac{27}{10}x+\frac{21\times 190}{50\times 7}+0.42\times \frac{5}{7}x+270.2=679$$

Do the multiplications in the fraction \frac{21\times 190}{50\times 7}.

$$\frac{486}{5}+\frac{27}{10}x+\frac{3990}{350}+0.42\times \frac{5}{7}x+270.2=679$$

Reduce the fraction \frac{3990}{350} to lowest terms by extracting and canceling out 70.

$$\frac{486}{5}+\frac{27}{10}x+\frac{57}{5}+0.42\times \frac{5}{7}x+270.2=679$$

Convert decimal number 0.42 to fraction \frac{42}{100}. Reduce the fraction \frac{42}{100} to lowest terms by extracting and canceling out 2.

$$\frac{486}{5}+\frac{27}{10}x+\frac{57}{5}+\frac{21}{50}\times \frac{5}{7}x+270.2=679$$

Multiply \frac{21}{50} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{486}{5}+\frac{27}{10}x+\frac{57}{5}+\frac{21\times 5}{50\times 7}x+270.2=679$$

Do the multiplications in the fraction \frac{21\times 5}{50\times 7}.

$$\frac{486}{5}+\frac{27}{10}x+\frac{57}{5}+\frac{105}{350}x+270.2=679$$

Reduce the fraction \frac{105}{350} to lowest terms by extracting and canceling out 35.

$$\frac{486}{5}+\frac{27}{10}x+\frac{57}{5}+\frac{3}{10}x+270.2=679$$

Since \frac{486}{5} and \frac{57}{5} have the same denominator, add them by adding their numerators.

$$\frac{486+57}{5}+\frac{27}{10}x+\frac{3}{10}x+270.2=679$$

Add 486 and 57 to get 543.

$$\frac{543}{5}+\frac{27}{10}x+\frac{3}{10}x+270.2=679$$

Combine \frac{27}{10}x and \frac{3}{10}x to get 3x.

$$\frac{543}{5}+3x+270.2=679$$

Convert decimal number 270.2 to fraction \frac{2702}{10}. Reduce the fraction \frac{2702}{10} to lowest terms by extracting and canceling out 2.

$$\frac{543}{5}+3x+\frac{1351}{5}=679$$

Since \frac{543}{5} and \frac{1351}{5} have the same denominator, add them by adding their numerators.

$$\frac{543+1351}{5}+3x=679$$

Add 543 and 1351 to get 1894.

$$\frac{1894}{5}+3x=679$$

Subtract \frac{1894}{5} from both sides.

$$3x=679-\frac{1894}{5}$$

Convert 679 to fraction \frac{3395}{5}.

$$3x=\frac{3395}{5}-\frac{1894}{5}$$

Since \frac{3395}{5} and \frac{1894}{5} have the same denominator, subtract them by subtracting their numerators.

$$3x=\frac{3395-1894}{5}$$

Subtract 1894 from 3395 to get 1501.

$$3x=\frac{1501}{5}$$

Divide both sides by 3.

$$x=\frac{\frac{1501}{5}}{3}$$

Express \frac{\frac{1501}{5}}{3} as a single fraction.

$$x=\frac{1501}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$x=\frac{1501}{15}$$