Solve for w. 6 - 7w = -9 + 8w w = ____

Gather Terms: First, we want to gather all the w terms on one side of the equation and the constant terms on the other side. We can do this by adding 7w to both sides of the equation to move the -7w term to the right side and by adding 9 to both sides of the equation to move the -9 to the left side. 6 - 7w + 7w + 9 = -9 + 8w + 7w + 9Combine Like Terms: Now, we simplify both sides of the equation by combining like terms. 6 + 9 = 15 and -7w + 8w = w, so the equation becomes: 15 = w + 9Isolate Variable: Next, we isolate w by subtracting 9 from both sides of the equation. 15 - 9 = w + 9 - 9Simplify and Solve: Finally, we simplify the left side of the equation to find the value of w. 15 - 9 = 6, so w = 6

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Solve for $w$ . $\newline$ $6 - 7w = -9 + 8w$ $\newline$ $w =$ __

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Algebra 1

Solve linear equations with variables on both sides

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Q. Solve for

w

\newline

6 - 7w = -9 + 8w

\newline

w =

Gather Terms: First, we want to gather all the $w$ terms on one side of the equation and the constant terms on the other side. We can do this by adding $7w$ to both sides of the equation to move the $-7w$ term to the right side and by adding $9$ to both sides of the equation to move the $-9$ to the left side. $6 - 7w + 7w + 9 = -9 + 8w + 7w + 9$
Combine Like Terms: Now, we simplify both sides of the equation by combining like terms. $\newline$ $6 + 9 = 15$ and $-7w + 8w = w$ , so the equation becomes: $\newline$ $15 = w + 9$
Isolate Variable: Next, we isolate $w$ by subtracting $9$ from both sides of the equation. $15 - 9 = w + 9 - 9$
Simplify and Solve: Finally, we simplify the left side of the equation to find the value of $w$ . $15 - 9 = 6$ , so $w = 6$