Answered

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What is the value of [tex]\( x \)[/tex] in the rational equation [tex]\( \frac{8}{2x} = \frac{12}{15} \)[/tex]?

A. 11.25
B. 10
C. 5
D. [tex]\( 6 \frac{2}{5} \)[/tex]

Sagot :

GinnyAnswer
To find the value of [tex]\( x \)[/tex] in the rational equation [tex]\(\frac{8}{2x} = \frac{12}{15}\)[/tex], follow these steps:

1. Write down the given equation:
[tex]\[ \frac{8}{2x} = \frac{12}{15} \][/tex]

2. Cross-multiply to eliminate the fractions:
[tex]\[ 8 \times 15 = 12 \times 2x \][/tex]

3. Calculate the products on both sides:
[tex]\[ 120 = 24x \][/tex]

4. Solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. To do this, divide both sides by 24:
[tex]\[ x = \frac{120}{24} \][/tex]

5. Simplify the fraction:
[tex]\[ x = 5 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex].

The correct answer is:
[tex]\[ 5 \][/tex]
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