To solve the equation [tex]\(\frac{4}{3} = \frac{x + 10}{15}\)[/tex] for [tex]\(x\)[/tex], we will follow a series of algebraic steps:
1. Eliminate the fraction on the right-hand side: To do this, we can start by multiplying both sides of the equation by 15. This step helps to clear the denominator on the right-hand side.
[tex]\[
15 \times \frac{4}{3} = 15 \times \frac{x + 10}{15}
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
15 \times \frac{4}{3} = x + 10
\][/tex]
2. Simplify the left-hand side: Now we need to calculate the left-hand side.
[tex]\[
15 \times \frac{4}{3} = \frac{15 \times 4}{3} = \frac{60}{3} = 20
\][/tex]
So the equation now becomes:
[tex]\[
20 = x + 10
\][/tex]
3. Isolate [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we need to subtract 10 from both sides.
[tex]\[
20 - 10 = x + 10 - 10
\][/tex]
Simplifying this, we get:
[tex]\[
10 = x
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{4}{3} = \frac{x + 10}{15}\)[/tex] is [tex]\(x = 10\)[/tex].
Among the given multiple choices, the correct answer is:
3) 10
