Solve for g. 1/6g + 3 = 4 - 1/3g g = ____

Combine like terms: First, we need to combine like terms by getting all the terms with g on one side and the constants on the other side. To do this, we can add 1/3g to both sides of the equation to move the term involving g from the right side to the left side. 1/6g + 3 + 1/3g = 4 - 1/3g + 1/3gSimplify the equation: Now, we simplify the equation by combining like terms. The terms with g combine to form 1/6g + 1/3g, and the constants on the right side cancel each other out. 1/6g + 1/3g + 3 = 4Find common denominator: To combine the fractions with g, we need a common denominator. The common denominator for 6 and 3 is 6, so we convert 1/3g to 2/6g. 1/6g + 2/6g + 3 = 4Add fractions with g: Now we add the fractions with g together. (1/6 + 2/6)g + 3 = 4 3/6g + 3 = 4Simplify fractions: We can simplify 3/6g to 1/2g since 3/6 reduces to 1/2. 1/2g + 3 = 4Isolate the term with g: Next, we need to isolate the term with g by subtracting 3 from both sides of the equation. 1/2g + 3 - 3 = 4 - 3 1/2g = 1Solve for g: To solve for g, we multiply both sides of the equation by 2 to cancel out the 1/2 factor on g. 2 * (1/2g) = 1 * 2 g = 2

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Solve for $g$ . $\newline$ $\frac{1}{6}g + 3 = 4 - \frac{1}{3}g$ $\newline$ g = ____

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for

g

\newline

\frac{1}{6}g + 3 = 4 - \frac{1}{3}g

\newline

g = ____

Combine like terms: First, we need to combine like terms by getting all the terms with $g$ on one side and the constants on the other side. To do this, we can add $\frac{1}{3}g$ to both sides of the equation to move the term involving $g$ from the right side to the left side. $\newline$ $\frac{1}{6}g + 3 + \frac{1}{3}g = 4 - \frac{1}{3}g + \frac{1}{3}g$
Simplify the equation: Now, we simplify the equation by combining like terms. The terms with $g$ combine to form $\frac{1}{6}g + \frac{1}{3}g$ , and the constants on the right side cancel each other out. $\frac{1}{6}g + \frac{1}{3}g + 3 = 4$
Find common denominator: To combine the fractions with $g$ , we need a common denominator. The common denominator for $6$ and $3$ is $6$ , so we convert $\frac{1}{3}g$ to $\frac{2}{6}g$ . $\newline$ $\frac{1}{6}g + \frac{2}{6}g + 3 = 4$
Add fractions with $g$ : Now we add the fractions with $g$ together. $\left(\frac{1}{6} + \frac{2}{6}\right)g + 3 = 4$ $\frac{3}{6}g + 3 = 4$
Simplify fractions: We can simplify $\frac{3}{6}g$ to $\frac{1}{2}g$ since $\frac{3}{6}$ reduces to $\frac{1}{2}$ . $\frac{1}{2}g + 3 = 4$
Isolate the term with $g$ : Next, we need to isolate the term with $g$ by subtracting $3$ from both sides of the equation. $\frac{1}{2}g + 3 - 3 = 4 - 3$ $\frac{1}{2}g = 1$
Solve for g: To solve for g, we multiply both sides of the equation by $2$ to cancel out the $\frac{1}{2}$ factor on $g$ . $\newline$ $2 \times \left(\frac{1}{2}g\right) = 1 \times 2$ $\newline$ $g = 2$