solve the given equation for x
x-2/4+x+3/5=5/4
x-2/4+x+3/5=5/4
2x = 5/4 + 2/4 - 3/5
2x = 25/20 + 10/20 - 12/20
2x = 24/20
x = 24/20 * 2/1
x = 48/20 = 2 8/20 = 2 2/5
Check my figures.
you said that x=22/5 correctt
I meant 2 and 2/5 or 2.4
i got 2x=23/20
I'm sorry, you're right. I guess I forgot how to subtract.
2x = 23/20
so what does that make x equal to
2x = 23/20
x = (23/20) / 2
x = (23/20) * 1/2
x = ?
x=23/40
Right.
To solve this equation for x, we need to simplify both sides of the equation and isolate the variable x.
Let's start by simplifying the equation step by step:
1. Combine like terms on the left side of the equation:
(x - 2)/4 + (x + 3)/5 = 5/4
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 4 and 5 is 20.
2. Generate equivalent fractions with the common denominator:
[(x - 2)(5) + (x + 3)(4)] / (4)(5) = 5/4
Multiply the numerator of the first fraction by 5 and the numerator of the second fraction by 4.
3. Expand the equation:
[5x - 10 + 4x + 12] / 20 = 5/4
Distribute the multiplication to each term in the numerators.
4. Combine like terms in the numerator:
(9x + 2) / 20 = 5/4
5. Multiply both sides of the equation by the common denominator (20) to eliminate the fraction:
20 * [(9x + 2) / 20] = (5/4) * 20
The left side of the equation cancels out, leaving us with:
9x + 2 = 25
6. Solve for x:
Subtract 2 from both sides of the equation:
9x + 2 - 2 = 25 - 2
9x = 23
7. Divide both sides of the equation by 9 to isolate x:
9x/9 = 23/9
x = 23/9
Therefore, the solution to the equation x - 2/4 + x + 3/5 = 5/4 is x = 23/9.