Solve 3.6x(-17.5)-0.2*7.5+36x=5/4-62*1/4

$$3.6 x ( - 17.5 ) - 0.2 \times 7.5 + 36 x = \frac { 5 } { 4 } - 62 \times \frac { 1 } { 4 }$$

Solve for x

$$x=\frac{17}{36}\approx 0.472222222$$

Steps for Solving Linear Equation

Multiply 3.6 and -17.5 to get -63.

$$-63x-0.2\times 7.5+36x=\frac{5}{4}-62\times \frac{1}{4}$$

Multiply 0.2 and 7.5 to get 1.5.

$$-63x-1.5+36x=\frac{5}{4}-62\times \frac{1}{4}$$

Combine -63x and 36x to get -27x.

$$-27x-1.5=\frac{5}{4}-62\times \frac{1}{4}$$

Multiply 62 and \frac{1}{4} to get \frac{62}{4}.

$$-27x-1.5=\frac{5}{4}-\frac{62}{4}$$

Reduce the fraction \frac{62}{4} to lowest terms by extracting and canceling out 2.

$$-27x-1.5=\frac{5}{4}-\frac{31}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{31}{2} to fractions with denominator 4.

$$-27x-1.5=\frac{5}{4}-\frac{62}{4}$$

Since \frac{5}{4} and \frac{62}{4} have the same denominator, subtract them by subtracting their numerators.

$$-27x-1.5=\frac{5-62}{4}$$

Subtract 62 from 5 to get -57.

$$-27x-1.5=-\frac{57}{4}$$

Add 1.5 to both sides.

$$-27x=-\frac{57}{4}+1.5$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$-27x=-\frac{57}{4}+\frac{3}{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{57}{4} and \frac{3}{2} to fractions with denominator 4.

$$-27x=-\frac{57}{4}+\frac{6}{4}$$

Since -\frac{57}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$-27x=\frac{-57+6}{4}$$

Add -57 and 6 to get -51.

$$-27x=-\frac{51}{4}$$

Divide both sides by -27.

$$x=\frac{-\frac{51}{4}}{-27}$$

Express \frac{-\frac{51}{4}}{-27} as a single fraction.

$$x=\frac{-51}{4\left(-27\right)}$$

Multiply 4 and -27 to get -108.

$$x=\frac{-51}{-108}$$

Reduce the fraction \frac{-51}{-108} to lowest terms by extracting and canceling out -3.

$$x=\frac{17}{36}$$