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Solve for x.

[tex]\(\frac{7}{x-4} = \frac{3}{5}\)[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(\frac{7}{x-4} = \frac{3}{5}\)[/tex], we will proceed with the following steps:

1. Cross-multiply the fractions to eliminate the denominators:

[tex]\[ \frac{7}{x-4} = \frac{3}{5} \][/tex]

Cross-multiplying gives us:

[tex]\[ 7 \cdot 5 = 3 \cdot (x - 4) \][/tex]

2. Simplify the equation:

[tex]\[ 35 = 3(x - 4) \][/tex]

3. Distribute the 3 on the right-hand side:

[tex]\[ 35 = 3x - 12 \][/tex]

4. Isolate the variable [tex]\(x\)[/tex]:

Add 12 to both sides of the equation to get rid of the constant term on the right-hand side.

[tex]\[ 35 + 12 = 3x - 12 + 12 \][/tex]

Simplifying this, we have:

[tex]\[ 47 = 3x \][/tex]

5. Solve for [tex]\(x\)[/tex]:

Divide both sides of the equation by 3 to isolate [tex]\(x\)[/tex].

[tex]\[ x = \frac{47}{3} \][/tex]

Therefore, the solution to the equation [tex]\(\frac{7}{x - 4} = \frac{3}{5}\)[/tex] is:

[tex]\[ x = \frac{47}{3} \][/tex]
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