14.7k views
1 vote
What is the value of x in the expression 4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5)?

A. 8/11
B. 13/4
C. 2/3
D. 5/8

User Kalida
by
7.2k points

1 Answer

3 votes

Final answer:

To solve for x in the expression 4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5), simplify the equation by converting mixed numbers to fractions, distribute the fractions, combine like terms, and isolate the variable.

Step-by-step explanation:

To solve for x in the expression 4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5), we need to simplify the equation step by step.

First, let's simplify the fractions in the equation. Convert the mixed numbers to improper fractions:

4 3/10 = 43/10, 2 2/5 = 12/5, and 5 1/2 = 11/2.

Now, distribute the fractions inside the parentheses:

4 3/10 - (2 2/5x + 5 1/2) = 1/2(-3 3/5x + 1 1/5)

43/10 - (12/5x + 11/2) = (1/2)(-18/5x + 6/5)

Simplify further:

43/10 - (12/5x + 11/2) = -9/5x + 3/5

Next, combine like terms:

43/10 - (24/10x + 55/10) = -9/5x + 3/5

43/10 - 79/10 - 24/10x = -9/5x + 3/5

-36/10x = -9/5x + 3/5

To get rid of the denominators, multiply both sides by 10:

-36x = -18x + 6

Now, let's isolate the variable:

-36x + 18x = 6

-18x = 6

Divide both sides by -18:

x = -6/18

Simplify the fraction:

x = -1/3

So, the value of x in the expression is -1/3.

User JRJurman
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories