Chapter 2: Q8. (page 106)

If $\frac{3 + x}{7 + x} = \frac{3}{7} + \frac{3}{7}$ , then $x =$ ?
$\begin{array}{l} A . \frac{3}{7} B.3 \\ C . 7D.21 \end{array}$

Short Answer

Expert verified

The value of x is21. Option D is correct.

Step by step solution

Step-1 – Apply the concept of addition of fractions

The two fractions are added when their denominator are same. To add the fractions with same denominator, add the numerator of the fractions. When denominators are not same, take the least common multiple and make it same.

Step-2 –Add the fractions

Consider the provided expression.

$\frac{3 + x}{7 + x} = \frac{3}{7} + \frac{3}{7}$

Add the fractions on right hand side of the expression.

Since, the denominator is same so just add the numerator.

$\begin{matrix} \frac{3 + x}{7 + x} = \frac{3}{7} + \frac{3}{7} \\ \frac{3 + x}{7 + x} = \frac{3 + 3}{7} \\ \frac{3 + x}{7 + x} = \frac{6}{7} \end{matrix}$

Step-3 – Simplify the expression

Cross multiply the terms.

Multiply 6 with $7 + x$ and 7 with $3 + x$ .

$\begin{matrix} 7 (3 + x) = 6 (7 + x) \\ 21 + 7 x = 42 + 6 x \end{matrix}$

Rearrange the terms and simply. Combine the like terms.

$\begin{matrix} 7 (3 + x) = 6 (7 + x) \\ 21 + 7 x = 42 + 6 x \\ 7 x - 6 x = 42 - 21 \\ x = 21 \end{matrix}$

Hence, the value of x is 21.

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.

Column A	Column B
Cost of one apple	Cost of one banana

If $\frac{3 + x}{7 + x} = \frac{3}{7} + \frac{3}{7}$ , then $x =$ ?
$\begin{array}{l} A . \frac{3}{7} B.3 \\ C . 7D.21 \end{array}$

Short Answer

Step by step solution

Step-1 – Apply the concept of addition of fractions

Step-2 –Add the fractions

Step-3 – Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Decision Maths

Applied Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If 3+x7+x=37+37, then x=?A.37B.3C.7D.21

Short Answer

Step by step solution

Step-1 – Apply the concept of addition of fractions

Step-2 –Add the fractions

Step-3 – Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Decision Maths

Applied Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If $\frac{3 + x}{7 + x} = \frac{3}{7} + \frac{3}{7}$ , then $x =$ ?
$\begin{array}{l} A . \frac{3}{7} B.3 \\ C . 7D.21 \end{array}$