Solve for j. -2 + 3/4j + 1/2j = 2j j = ____

Combine Like Terms: Combine like terms that contain the variable j on the left side of the equation. -2 + (3/4 + 1/2)j = 2j To combine the fractions, find a common denominator, which is 4. -2 + (3/4 + 2/4)j = 2j -2 + (5/4)j = 2jFind Common Denominator: Now, we want to get all the terms with j on one side and the constant terms on the other side. Let's move the (5/4)j term to the right side by subtracting it from both sides. -2 = 2j - (5/4)j To subtract the fractions, they need to have the same denominator. The common denominator is 4, so we convert 2j to (8/4)j. -2 = (8/4)j - (5/4)jMove Terms to Respective Sides: Subtract the j terms on the right side. -2 = (8/4 - 5/4)j -2 = (3/4)jSubtract Terms: To solve for j, divide both sides by (3/4), which is the same as multiplying by the reciprocal, 4/3. -2 * (4/3) = (3/4)j * (4/3) -8/3 = j

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Solve for $j$ . $\newline$ $-2 + \frac{3}{4}j + \frac{1}{2}j = 2j$ $\newline$ j = ____

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for

j

\newline

-2 + \frac{3}{4}j + \frac{1}{2}j = 2j

\newline

j = ____

Combine Like Terms: Combine like terms that contain the variable $j$ on the left side of the equation. $-2 + (\frac{3}{4} + \frac{1}{2})j = 2j$ To combine the fractions, find a common denominator, which is $4$ . $-2 + (\frac{3}{4} + \frac{2}{4})j = 2j$ $-2 + (\frac{5}{4})j = 2j$
Find Common Denominator: Now, we want to get all the terms with $j$ on one side and the constant terms on the other side. Let's move the $(5/4)j$ term to the right side by subtracting it from both sides. $\newline$ $-2 = 2j - (5/4)j$ $\newline$ To subtract the fractions, they need to have the same denominator. The common denominator is $4$ , so we convert $2j$ to $(8/4)j$ . $\newline$ $-2 = (8/4)j - (5/4)j$
Move Terms to Respective Sides: Subtract the $j$ terms on the right side. $\newline$ $-2 = \left(\frac{8}{4} - \frac{5}{4}\right)j$ $\newline$ $-2 = \left(\frac{3}{4}\right)j$
Subtract Terms: To solve for $j$ , divide both sides by $(3/4)$ , which is the same as multiplying by the reciprocal, $4/3$ . $-2 \times (4/3) = (3/4)j \times (4/3)$ $-8/3 = j$