Question

In the following exercises, solve each equation with decimal coefficients.

$0.9x-1.25=0.75x+1.75$

Short answer

The value of $x$is$20$

Step-by-step solution

Step 1. Given Information 

In the given question we have to solve equation with decimal coefficients.
$0.9x-1.25=0.75x+1.75$

Step 2. The given equation is 0.9x−1.25=0.75x+1.75

Now we solve the given equation for the value of$x$

Looking at the decimals and thinking of the equivalent fractions:

$0.9=\frac{9}{10}1.25=\frac{125}{100}0.75=\frac{75}{100}1.75=\frac{175}{100}$

The LCD is 100.

Step 4. By multiplying by the LCD we will clear the decimals from the equation. 

To clear decimals, multiply by 100.

$100(0.9x-1.25)=100(0.75x+1.75)$

Distribute first.

$$\begin{gathered} 100\times 0.9x-100\times 1.25=100\times 0.75x+100\times 1.75 \\ 90x-125=75x+175 \end{gathered}$$

Step 5. Subtract 75x on both side 

$$\begin{gathered} 90x-125-75x=75x+175-75x \\ 15x-125=175 \end{gathered}$$

Add $125$on both side

$$\begin{gathered} 15x-125+125=175+125 \\ 15x=300 \\ \frac{15}{15}x=\frac{300}{15} \\ x=20 \end{gathered}$$

Step 6. Now checking the value. 

putting $x=20$in the given equation

$$\begin{gathered} 0.9\times 20-1.25=0.75\times 20+1.75 \\ 18-1.25=15+1.75 \\ 16.75=16.75 \end{gathered}$$