Chapter 2: Q. 67 (page 112)

In the following exercises, solve each equation with decimal coefficients.
$0.9 x - 1.25 = 0.75 x + 1.75$

Short Answer

Expert verified

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.
$0.9 x - 1.25 = 0.75 x + 1.75$

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.

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

Distribute first.

$100 \times 0.9 x - 100 \times 1.25 = 100 \times 0.75 x + 100 \times 1.75 90 x - 125 = 75 x + 175$

Step 5. Subtract 75x on both side

$90 x - 125 - 75 x = 75 x + 175 - 75 x 15 x - 125 = 175$

Add $125$ on both side

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

Step 6. Now checking the value.

putting $x = 20$ in the given equation

$0.9 \times 20 - 1.25 = 0.75 \times 20 + 1.75 18 - 1.25 = 15 + 1.75 16.75 = 16.75$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve each equation with decimal coefficients.
$0.9 x - 1.25 = 0.75 x + 1.75$

Short Answer

Step by step solution

Step 1. Given Information

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

Looking at the decimals and thinking of the equivalent fractions:

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

Step 5. Subtract 75x on both side

Step 6. Now checking the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each equation with decimal coefficients.0.9x−1.25=0.75x+1.75

Short Answer

Step by step solution

Step 1. Given Information

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

Looking at the decimals and thinking of the equivalent fractions:

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

Step 5. Subtract 75x on both side

Step 6. Now checking the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Geometry

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each equation with decimal coefficients.
$0.9 x - 1.25 = 0.75 x + 1.75$