Certainly! Let's solve for [tex]\( x \)[/tex] in the given expression:
[tex]\[
\frac{64 \sqrt{x}}{112}
\][/tex]
First, we simplify the fraction:
[tex]\[
\frac{64}{112}
\][/tex]
We can simplify [tex]\(\frac{64}{112}\)[/tex] by finding the greatest common divisor (GCD) of 64 and 112, which is 16:
[tex]\[
\frac{64}{112} = \frac{64 \div 16}{112 \div 16} = \frac{4}{7}
\][/tex]
So, the given expression simplifies to:
[tex]\[
\frac{64 \sqrt{x}}{112} = \frac{4 \sqrt{x}}{7}
\][/tex]
Next, let's express this simplified form more clearly:
[tex]\[
4 \sqrt{x} / 7
\][/tex]
Let's assume this entire expression is equal to some constant [tex]\( K \)[/tex]. For simplicity, let's assume [tex]\( K = 1 \)[/tex]:
[tex]\[
4 \sqrt{x} / 7 = 1
\][/tex]
To isolate [tex]\(\sqrt{x}\)[/tex], we multiply both sides by 7:
[tex]\[
4 \sqrt{x} = 7
\][/tex]
Next, we divide both sides by 4 to solve for [tex]\(\sqrt{x}\)[/tex]:
[tex]\[
\sqrt{x} = \frac{7}{4}
\][/tex]
Now, we square both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
(\sqrt{x})^2 = \left(\frac{7}{4}\right)^2
\][/tex]
[tex]\[
x = \left(\frac{7}{4}\right)^2
\][/tex]
[tex]\[
x = \frac{49}{16}
\][/tex]
Converting [tex]\(\frac{49}{16}\)[/tex] to a decimal:
[tex]\[
x = 3.0625
\][/tex]
Thus, the final solution for [tex]\( x \)[/tex] is:
[tex]\[
x = 3.0625
\][/tex]
And that is the detailed, step-by-step solution for finding [tex]\( x \)[/tex] in the given expression.
