Solve for k. 5/3k - 3 = 1/3 + 2k k = ____

Rearrange terms: First, we want to get all the terms with k on one side and the constant terms on the other side. 5/3k - 3 = 1/3 + 2k To do this, we can start by adding 3 to both sides to get rid of the -3 on the left side. 5/3k - 3 + 3 = 1/3 + 2k + 3Simplify equation: Now we simplify both sides of the equation. 5/3k = 1/3 + 2k + 3 To combine the constant terms on the right side, we need to find a common denominator, which is 3. 5/3k = (1 + 9)/3 + 2kCombine constant terms: Next, we add the fractions on the right side. 5/3k = 10/3 + 2k Now we want to get all the k terms on one side. We can subtract 2k from both sides to move the k terms to the left side. 5/3k - 2k = 10/3Move k terms: We need to express 2k with a denominator of 3 to combine it with 5/3k. 5/3k - (2k * (3/3)) = 10/3 5/3k - 6/3k = 10/3 Now we combine the k terms on the left side. (5 - 6)/3k = 10/3 -1/3k = 10/3Combine k terms: To solve for k, we need to get rid of the fraction. We can multiply both sides by -3 to do this. -3 * (-1/3k) = -3 * (10/3) This simplifies to: k = -10

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Solve for $k$ . $\newline$ $\frac{5}{3}k - 3 = \frac{1}{3} + 2k$ $\newline$ $k =$ __

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for

k

\newline

\frac{5}{3}k - 3 = \frac{1}{3} + 2k

\newline

k =

Rearrange terms: First, we want to get all the terms with $k$ on one side and the constant terms on the other side. $\frac{5}{3}k - 3 = \frac{1}{3} + 2k$ To do this, we can start by adding $3$ to both sides to get rid of the $-3$ on the left side. $\frac{5}{3}k - 3 + 3 = \frac{1}{3} + 2k + 3$
Simplify equation: Now we simplify both sides of the equation. $\newline$ $\frac{5}{3}k = \frac{1}{3} + 2k + 3$ $\newline$ To combine the constant terms on the right side, we need to find a common denominator, which is $3$ . $\newline$ $\frac{5}{3}k = \frac{(1 + 9)}{3} + 2k$
Combine constant terms: Next, we add the fractions on the right side. $\newline$ $\frac{5}{3}k = \frac{10}{3} + 2k$ $\newline$ Now we want to get all the $k$ terms on one side. We can subtract $2k$ from both sides to move the $k$ terms to the left side. $\newline$ $\frac{5}{3}k - 2k = \frac{10}{3}$
Move $k$ terms: We need to express $2k$ with a denominator of $3$ to combine it with $\frac{5}{3}k$ .
$\frac{5}{3}k - (2k \times (\frac{3}{3})) = \frac{10}{3}$
$\frac{5}{3}k - \frac{6}{3}k = \frac{10}{3}$
Now we combine the $k$ terms on the left side.
$(\frac{5 - 6}{3})k = \frac{10}{3}$
$-\frac{1}{3}k = \frac{10}{3}$
Combine $k$ terms: To solve for $k$ , we need to get rid of the fraction. We can multiply both sides by $-3$ to do this. $\newline$ -3 \times (-\frac{1}{3}k) = -3 \times (\frac{10}{3})$\newlineThis simplifies to: $\newline$ \$k = -10$