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$Solve for z. Express your answer as a proper or improper fraction in simplest terms. -(1)/(2)+(7)/(10)z=-(1)/(3) Answer: z=$

Solve for $z$ . Express your answer as a proper or improper fraction in simplest terms. $\newline$ $-\frac{1}{2}+\frac{7}{10} z=-\frac{1}{3}$ $\newline$ Answer: $z=$

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Multiplication with rational exponents

Full solution

Q. Solve for

z

. Express your answer as a proper or improper fraction in simplest terms.

\newline

-\frac{1}{2}+\frac{7}{10} z=-\frac{1}{3}

\newline

Answer:

z=

Isolate z term: Isolate the term containing z. $\newline$ To isolate the term with z, we need to move the constant term to the other side of the equation by adding $\frac{1}{2}$ to both sides. $\newline$ $-\frac{1}{2} + \frac{7}{10}z + \frac{1}{2} = -\frac{1}{3} + \frac{1}{2}$
Calculate sum on right side: Calculate the sum on the right side of the equation. $\newline$ We need to find a common denominator to add the fractions on the right side. The common denominator for $3$ and $2$ is $6$ . $\newline$ $-(1)/(3) + (1)/(2) = -(2)/(6) + (3)/(6) = (1)/(6)$
Simplify left side: Simplify the left side of the equation. $\newline$ The constant terms on the left side cancel each other out, leaving us with: $\newline$ $(\frac{7}{10}z = \frac{1}{6})$
Solve for z: Solve for z. $\newline$ To solve for z, we need to divide both sides of the equation by $(\frac{7}{10})$ , which is the coefficient of z. $\newline$ $z = \frac{1}{6} \div \frac{7}{10}$
Perform division: Perform the division to find $z$ . $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ $z = \frac{1}{6} \times \frac{10}{7}$ $\newline$ $z = \frac{10}{42}$
Simplify fraction: Simplify the fraction. $\newline$ The fraction $(10)/(42)$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $z = (10/2)/(42/2)$ $\newline$ $z = (5)/(21)$

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