Question

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

$1.2x-0.91=0.8x+2.29$

Short answer

The value of $x$is$8$

Step-by-step solution

Step 1. Given Information 

In the given question we have to solve equation with decimal coefficients.
$1.2x-0.91=0.8x+2.29$

Step 2. The given equation is 1.2x−0.91=0.8x+2.29

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

Looking at the decimals and thinking of the equivalent fractions:

$0.8=\frac{8}{10}1.2=\frac{12}{10}0.91=\frac{91}{100}2.29=\frac{229}{100}$

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.

$100(1.2x-0.91)=100(0.8x+2.29)$

Distribute first.

$$\begin{gathered} 100\times 1.2x-100\times 0.91=100\times 0.8x+100\times 2.29 \\ 120x-91=80x+229 \end{gathered}$$

Step 5. Subtract 80x on both side 

$$\begin{gathered} 120x-91-80x=80x+229-80x \\ 40x-91=229 \end{gathered}$$

Add 91 on both side

role="math" localid="1645508107719" $$\begin{gathered} 40x-91+91=229+91 \\ 40x=320 \\ \frac{40}{40}x=\frac{320}{40} \\ x=8 \end{gathered}$$

Step 6. Now checking the value. 

putting $x=8$in the given equation

$$\begin{gathered} 1.2\times 8-0.91=0.8\times 8+2.29 \\ 9.6-0.91=6.4+2.29 \\ 8.69=8.69 \end{gathered}$$