Good evening. I have a math problem I need some help with please.
1/2 (3/5 X - 8) + 7/4 (2/5 X + 4)
X is a variable.
My answer that I have so far is:
3/10 X - 4 + 7/10 X and then I get stuck.
combine like terms ... and you're finished
Good evening! I'll be happy to help you with your math problem.
Let's go step by step to simplify the expression:
1. Start by simplifying within the parentheses:
3/5 * x - 8
2. Distribute the 1/2 to the expression within the first set of parentheses and distribute the 7/4 to the expression within the second set of parentheses:
1/2 * (3/5 * x - 8) + 7/4 * (2/5 * x + 4)
Simplifying the first part:
(1/2 * 3/5 * x) - (1/2 * 8)
3/10 * x - 4
Simplifying the second part:
(7/4 * 2/5 * x) + (7/4 * 4)
14/20 * x + 28/4
3. Combine the two simplified expressions:
(3/10 * x - 4) + (14/20 * x + 28/4)
4. Combine like terms:
3/10 * x + 14/20 * x - 4 + 28/4
To combine the fractions with the variable, we need to find a common denominator:
The common denominator for 10 and 20 is 20, so multiply the first fraction by 2/2 and the second fraction by 1/1:
6/20 * x + 14/20 * x - 4 + 28/4
Simplify the fractions:
6/20 * x is equivalent to 3/10 * x, and 14/20 * x is equivalent to 7/10 * x:
3/10 * x + 7/10 * x - 4 + 28/4
5. Combine like terms again:
3/10 * x + 7/10 * x is equal to (3/10 + 7/10) * x:
(3/10 + 7/10) * x - 4 + 28/4
The sum of 3/10 and 7/10 is 10/10, which simplifies to 1, so we have:
1 * x - 4 + 28/4
6. Simplify the expression remaining:
x - 4 + 7
7. Combining the terms:
x - 4 + 7 is equal to x + 3
So, the final simplified expression is x + 3.