Find the positive solution of the equation. 6x^((7)/(8))+19=787 Answer:

Isolate variable term: Isolate the term with the variable. Subtract 19 from both sides of the equation to isolate the term with the variable $x$. $6x^{\frac{7}{8}} + 19 - 19 = 787 - 19$ $6x^{\frac{7}{8}} = 768$Divide by 6: Divide both sides by 6 to solve for $x^{\frac{7}{8}}$. $\frac{6x^{\frac{7}{8}}}{6} = \frac{768}{6}$ $x^{\frac{7}{8}} = 128$Recognize power of 2: Recognize that 128 is a power of 2. $128 = 2^7$Substitute value: Substitute $2^7$ for 128 in the equation. $x^{\frac{7}{8}} = 2^7$Raise to power: Raise both sides of the equation to the power of $\frac{8}{7}$ to solve for $x$. $(x^{\frac{7}{8}})^{\frac{8}{7}} = (2^7)^{\frac{8}{7}}$ $x = 2^8$Calculate value: Calculate $2^8$ to find the value of $x$. $2^8 = 256$

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Q. Find the positive solution of the equation.

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6 x^{\frac{7}{8}}+19=787

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Answer:

Isolate variable term: Isolate the term with the variable. $\newline$ Subtract $19$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $6x^{\frac{7}{8}} + 19 - 19 = 787 - 19$ $\newline$ $6x^{\frac{7}{8}} = 768$
Divide by $6$ : Divide both sides by $6$ to solve for $x^{\frac{7}{8}}$ . $\newline$ $\frac{6x^{\frac{7}{8}}}{6} = \frac{768}{6}$ $\newline$ $x^{\frac{7}{8}} = 128$
Recognize power of $2$ : Recognize that $128$ is a power of $2$ . $\newline$ $128 = 2^7$
Substitute value: Substitute $2^7$ for $128$ in the equation. $\newline$ $x^{\frac{7}{8}} = 2^7$
Raise to power: Raise both sides of the equation to the power of $\frac{8}{7}$ to solve for $x$ . $\newline$ $(x^{\frac{7}{8}})^{\frac{8}{7}} = (2^7)^{\frac{8}{7}}$ $\newline$ $x = 2^8$
Calculate value: Calculate $2^8$ to find the value of $x$ . $\newline$ $2^8 = 256$