Solve 80x-1800+12/100(x-14.5)=180

$$80 x - 1800 + \frac { 12 } { 100 } ( x - 14.5 ) = 180$$

Solve for x

$$x = \frac{99087}{4006} = 24\frac{2943}{4006} \approx 24.734648028$$

Steps for Solving Linear Equation

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$80x-1800+\frac{3}{25}\left(x-14.5\right)=180$$

Use the distributive property to multiply \frac{3}{25} by x-14.5.

$$80x-1800+\frac{3}{25}x+\frac{3}{25}\left(-14.5\right)=180$$

Convert decimal number -14.5 to fraction -\frac{145}{10}. Reduce the fraction -\frac{145}{10} to lowest terms by extracting and canceling out 5.

$$80x-1800+\frac{3}{25}x+\frac{3}{25}\left(-\frac{29}{2}\right)=180$$

Multiply \frac{3}{25} times -\frac{29}{2} by multiplying numerator times numerator and denominator times denominator.

$$80x-1800+\frac{3}{25}x+\frac{3\left(-29\right)}{25\times 2}=180$$

Do the multiplications in the fraction \frac{3\left(-29\right)}{25\times 2}.

$$80x-1800+\frac{3}{25}x+\frac{-87}{50}=180$$

Fraction \frac{-87}{50} can be rewritten as -\frac{87}{50} by extracting the negative sign.

$$80x-1800+\frac{3}{25}x-\frac{87}{50}=180$$

Combine 80x and \frac{3}{25}x to get \frac{2003}{25}x.

$$\frac{2003}{25}x-1800-\frac{87}{50}=180$$

Convert -1800 to fraction -\frac{90000}{50}.

$$\frac{2003}{25}x-\frac{90000}{50}-\frac{87}{50}=180$$

Since -\frac{90000}{50} and \frac{87}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2003}{25}x+\frac{-90000-87}{50}=180$$

Subtract 87 from -90000 to get -90087.

$$\frac{2003}{25}x-\frac{90087}{50}=180$$

Add \frac{90087}{50} to both sides.

$$\frac{2003}{25}x=180+\frac{90087}{50}$$

Convert 180 to fraction \frac{9000}{50}.

$$\frac{2003}{25}x=\frac{9000}{50}+\frac{90087}{50}$$

Since \frac{9000}{50} and \frac{90087}{50} have the same denominator, add them by adding their numerators.

$$\frac{2003}{25}x=\frac{9000+90087}{50}$$

Add 9000 and 90087 to get 99087.

$$\frac{2003}{25}x=\frac{99087}{50}$$

Multiply both sides by \frac{25}{2003}, the reciprocal of \frac{2003}{25}.

$$x=\frac{99087}{50}\times \frac{25}{2003}$$

Multiply \frac{99087}{50} times \frac{25}{2003} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{99087\times 25}{50\times 2003}$$

Do the multiplications in the fraction \frac{99087\times 25}{50\times 2003}.

$$x=\frac{2477175}{100150}$$

Reduce the fraction \frac{2477175}{100150} to lowest terms by extracting and canceling out 25.

$$x=\frac{99087}{4006}$$