Question

question
. solve for x and simplify the answer fully.
\\(\frac{x + 5}{3} = \frac{x - 5}{2}\\)
answer attempt 1 out of 2
\\(x = \square\\) submit answer

Explanation:

Step1: Cross - multiply to eliminate denominators

To solve the equation \(\frac{x + 5}{3}=\frac{x - 5}{2}\), we cross - multiply. Cross - multiplying gives us \(2(x + 5)=3(x - 5)\). This is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(ad = bc\) (where \(b
eq0\) and \(d
eq0\)).

Step2: Expand both sides

Expanding the left - hand side: \(2(x + 5)=2x+10\) (using the distributive property \(a(b + c)=ab+ac\) with \(a = 2\), \(b=x\), and \(c = 5\)).
Expanding the right - hand side: \(3(x - 5)=3x-15\) (using the distributive property \(a(b - c)=ab - ac\) with \(a = 3\), \(b=x\), and \(c = 5\)).
So our equation becomes \(2x + 10=3x-15\).

Step3: Isolate the variable \(x\)

Subtract \(2x\) from both sides of the equation: \(2x+10 - 2x=3x-15 - 2x\).
Simplifying both sides, we get \(10=x - 15\).
Then add 15 to both sides: \(10 + 15=x-15 + 15\).
Simplifying, we find that \(x = 25\).

Answer:

\(25\)