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Solve for \( x \):

[tex]\[ \frac{x}{x+26} = \frac{x}{3x-32} \][/tex]

[tex]\[ x = [?] \][/tex]

Sagot :

GinnyAnswer
Sure, let's solve the equation step-by-step. We are given the equation:

[tex]\[ x + 26 = 3x - 32 \][/tex]

We need to solve for \( x \). Here's how we do it:

1. Isolate the terms involving \( x \) on one side of the equation:

Subtract \( x \) from both sides to begin isolating \( x \):

[tex]\[ x + 26 - x = 3x - 32 - x \][/tex]

This simplifies to:

[tex]\[ 26 = 2x - 32 \][/tex]

2. Isolate the constant term:

Add 32 to both sides to separate the constant term:

[tex]\[ 26 + 32 = 2x - 32 + 32 \][/tex]

This simplifies to:

[tex]\[ 58 = 2x \][/tex]

3. Solve for \( x \):

Divide both sides by 2:

[tex]\[ \frac{58}{2} = \frac{2x}{2} \][/tex]

This simplifies to:

[tex]\[ 29 = x \][/tex]

Therefore, the solution to the equation \( x + 26 = 3x - 32 \) is:

[tex]\[ x = 29 \][/tex]
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