Solve for z. {:[(z-6)/(2z+1)=10],[z=]:}

Set up equation: Set up the equation from the problem. (z-6)/(2z+1) = 10Eliminate fraction: Multiply both sides of the equation by (2z+1) to eliminate the fraction. (z-6)/(2z+1) * (2z+1) = 10 * (2z+1) z - 6 = 20z + 10Move z terms: Move all z terms to one side of the equation by subtracting 20z from both sides. z - 20z - 6 = 20z - 20z + 10 -19z - 6 = 10Move constant term: Move the constant term to the other side by adding 6 to both sides. -19z - 6 + 6 = 10 + 6 -19z = 16Divide by -19: Divide both sides by -19 to solve for z. -19z / -19 = 16 / -19 z = -16/19

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Math Problems

Grade 6

Multiply two decimals: where does the decimal point go?

Full solution

Q. Solve for

z

\newline

\begin{array}{l} \frac{z-6}{2 z+1}=10 \\ z= \end{array}

Set up equation: Set up the equation from the problem. $\frac{z-6}{2z+1} = 10$
Eliminate fraction: Multiply both sides of the equation by $(2z+1)$ to eliminate the fraction. $\frac{z-6}{2z+1} \times (2z+1) = 10 \times (2z+1)$ $z - 6 = 20z + 10$
Move z terms: Move all z terms to one side of the equation by subtracting $20z$ from both sides. $\newline$ $z - 20z - 6 = 20z - 20z + 10$ $\newline$ $-19z - 6 = 10$
Move constant term: Move the constant term to the other side by adding $6$ to both sides. $\newline$ $-19z - 6 + 6 = 10 + 6$ $\newline$ $-19z = 16$
Divide by $-19$ : Divide both sides by $-19$ to solve for z. $\newline$ $-19z / -19 = 16 / -19$ $\newline$ $z = -16/19$