Solve x-4.5/6.5-4.5=7.5/7-2

$$\frac { x - 4.5 } { 6.5 - 4.5 } = \frac { 7.5 } { 7 - 2 }$$

Solve for x

$$x=7.5$$

Steps for Solving Linear Equation

Subtract 4.5 from 6.5 to get 2.

$$\frac{x-4.5}{2}=\frac{7.5}{7-2}$$

Subtract 2 from 7 to get 5.

$$\frac{x-4.5}{2}=\frac{7.5}{5}$$

Expand \frac{7.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{x-4.5}{2}=\frac{75}{50}$$

Reduce the fraction \frac{75}{50} to lowest terms by extracting and canceling out 25.

$$\frac{x-4.5}{2}=\frac{3}{2}$$

Divide each term of x-4.5 by 2 to get \frac{1}{2}x-2.25.

$$\frac{1}{2}x-2.25=\frac{3}{2}$$

Add 2.25 to both sides.

$$\frac{1}{2}x=\frac{3}{2}+2.25$$

Convert decimal number 2.25 to fraction \frac{225}{100}. Reduce the fraction \frac{225}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{2}x=\frac{3}{2}+\frac{9}{4}$$

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

$$\frac{1}{2}x=\frac{6}{4}+\frac{9}{4}$$

Since \frac{6}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x=\frac{6+9}{4}$$

Add 6 and 9 to get 15.

$$\frac{1}{2}x=\frac{15}{4}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{15}{4}\times 2$$

Express \frac{15}{4}\times 2 as a single fraction.

$$x=\frac{15\times 2}{4}$$

Multiply 15 and 2 to get 30.

$$x=\frac{30}{4}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{15}{2}$$