Solve for j. -4j = 2/3j + 2 - 4j j = ____

Simplify the equation: First, let's simplify the equation by combining like terms on both sides. -4j = 2/3j + 2 - 4j Combine the -4j terms on the right side. -4j = (2/3j - 4j) + 2Combine j terms: Now, we need to combine the j terms on the right side. To do this, we need a common denominator. 2/3j - 4j can be written as 2/3j - (12/3)j, since 4j is the same as (12/3)j. -4j = (2/3 - 12/3)j + 2Subtract fractions: Next, subtract the fractions. -4j = (-10/3)j + 2 Now we have a simplified equation.Isolate j term: Since -4j is also on the left side, we can add (10/3)j to both sides to isolate the j term on the right. -4j + (10/3)j = 2 To combine the j terms on the left, we need a common denominator, which is 3. (-12/3)j + (10/3)j = 2Combine j terms: Combine the j terms on the left side. (-12/3 + 10/3)j = 2 (-2/3)j = 2Solve for j: To solve for j, divide both sides by (-2/3). j = 2 / (-2/3)Multiply numbers: Dividing by a fraction is the same as multiplying by its reciprocal. j = 2 * (-3/2)Now, multiply the numbers. j = -3

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Solve for $j$ . $\newline$ $-4j = \frac{2}{3}j + 2 - 4j$ $\newline$ $j =$ ____

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for

j

\newline

-4j = \frac{2}{3}j + 2 - 4j

\newline

j =

____

Simplify the equation: First, let's simplify the equation by combining like terms on both sides. $\newline$ $-4j = \frac{2}{3}j + 2 - 4j$ $\newline$ Combine the $-4j$ terms on the right side. $\newline$ $-4j = (\frac{2}{3}j - 4j) + 2$
Combine j terms: Now, we need to combine the j terms on the right side. To do this, we need a common denominator. $\newline$ $\frac{2}{3}j - 4j$ can be written as $\frac{2}{3}j - \left(\frac{12}{3}\right)j$ , since $4j$ is the same as $\left(\frac{12}{3}\right)j$ . $\newline$ $-4j = \left(\frac{2}{3} - \frac{12}{3}\right)j + 2$
Subtract fractions: Next, subtract the fractions. $\newline$ $-4j = \left(-\frac{10}{3}\right)j + 2$ $\newline$ Now we have a simplified equation.
Isolate j term: Since $-4j$ is also on the left side, we can add $(10/3)j$ to both sides to isolate the j term on the right. $\newline$ $-4j + (10/3)j = 2$ $\newline$ To combine the j terms on the left, we need a common denominator, which is $3$ . $\newline$ $(-12/3)j + (10/3)j = 2$
Combine j terms: Combine the $j$ terms on the left side. $\left(-\frac{12}{3} + \frac{10}{3}\right)j = 2$ $\left(-\frac{2}{3}\right)j = 2$
Solve for $j$ : To solve for $j$ , divide both sides by $(-\frac{2}{3})$ . $j = \frac{2}{(-\frac{2}{3})}$
Multiply numbers: Dividing by a fraction is the same as multiplying by its reciprocal. $j = 2 \times \left(-\frac{3}{2}\right)$
Multiply numbers: Dividing by a fraction is the same as multiplying by its reciprocal. $\newline$ $j = 2 \times \left(-\frac{3}{2}\right)$ Now, multiply the numbers. $\newline$ $j = -3$