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37

{:[-6(w-4)+8w=2(w+9)],[-6w+24+8w=2w+18]:}

$37$ $\newline$ $\begin{array}{l} -6(w-4)+8 w=2(w+9) \\ -6 w+24+8 w=2 w+18 \end{array}$

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Descartes' Rule of Signs

Full solution

Q.

37

\newline

\begin{array}{l} -6(w-4)+8 w=2(w+9) \\ -6 w+24+8 w=2 w+18 \end{array}

Simplify Equation: First, let's simplify the given equation by distributing the terms inside the brackets and combining like terms. $\newline$ $-6(w-4) + 8w = 2(w+9)$ $\newline$ Distribute $-6$ into $(w-4)$ and $2$ into $(w+9)$ : $\newline$ $-6w + 24 + 8w = 2w + 18$
Combine Like Terms: Now, let's combine the like terms on both sides of the equation. $\newline$ $(-6w + 8w) + 24 = 2w + 18$ $\newline$ $2w + 24 = 2w + 18$
Isolate Constant Terms: Next, we subtract $2w$ from both sides of the equation to isolate the constant terms. $\newline$ $2w + 24 - 2w = 2w + 18 - 2w$ $\newline$ $24 = 18$
Identify No Solution: We see that the equation simplifies to $24 = 18$ , which is not true. This means that there is no solution to the equation, as the variables have canceled out and we are left with a false statement.

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