Question

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

$0.7x+0.4=0.6x+2.4$

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.
$0.7x+0.4=0.6x+2.4$

Step 2. The given equation is 0.7x+0.4=0.6x+2.4

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

Looking at the decimals and thinking of the equivalent fractions:

$0.4=\frac{4}{10}0.6=\frac{6}{10}0.7=\frac{7}{10}2.4=\frac{24}{10}$

The LCD is 10.

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

To clear decimals, multiply by 10.

$10\left(0.7x+0.4\right)=10(0.6x+2.4)$

Distribute first.

$$\begin{gathered} 10\times 0.7x+10\times 0.4=10\times 0.6x+10\times 2.4 \\ 7x+4=6x+24 \end{gathered}$$

Step 5. Subtract 6x on both side 

$$\begin{gathered} 7x+4-6x=6x+24-6x \\ x+4=24 \end{gathered}$$

Subtract 4 on both side

$$\begin{gathered} x+4-4=24-4 \\ x=20 \end{gathered}$$

Step 6. Now checking the value. 

putting $x=20$in the given equation

$$\begin{gathered} 0.7\times 20+0.4=0.6\times 20+2.4 \\ 14+0.4=12+2.4 \\ 14.4=14.4 \end{gathered}$$