How many solutions does this equation have? –6w = –5w + 6 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable w: Isolate the variable w on one side of the equation. To do this, we can add 5w to both sides of the equation to get: –6w + 5w = –5w + 5w + 6 This simplifies to: –w = 6Solve for w: Solve for w. To isolate w, we multiply both sides of the equation by -1: –1 * (–w) = 6 * (–1) This simplifies to: w = –6Check the solution: Check the solution. We substitute w = –6 back into the original equation to verify if it holds true: –6 * (–6) = –5 * (–6) + 6 36 = 30 + 6 36 = 36 Since the equation holds true, our solution w = –6 is correct.

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How many solutions does this equation have? $\newline$ $-6w = -5w + 6$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does this equation have?

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-6w = -5w + 6

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Choices:

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(A)no solution

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(B)one solution

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(C)infinitely many solutions

Isolate variable w: Isolate the variable $w$ on one side of the equation. $\newline$ To do this, we can add $5w$ to both sides of the equation to get: $\newline$ $–6w + 5w = –5w + 5w + 6(\newline$ This simplifies to: $\newline$ \$–w = 6\)
Solve for w: Solve for w.$\newline$To isolate w, we multiply both sides of the equation by $-1$:$\newline$$-1 \times (\text{-}w) = 6 \times (\text{-}1)$$\newline$This simplifies to:$\newline$$w = \text{-}6$
Check the solution: Check the solution.$\newline$We substitute $w = -6$ back into the original equation to verify if it holds true:$\newline$$-6 \times (-6) = -5 \times (-6) + 6$$\newline$$36 = 30 + 6$$\newline$$36 = 36$$\newline$Since the equation holds true, our solution $w = -6$ is correct.