Challenge The measure of angleDBE is left parenthesis 0.3 x minus 31 right parenthesis degrees and the measure of angleCBE is left parenthesis 0.1 x minus 41 right parenthesis degrees. Find the value of x.

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Part 1
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Answer 1

To find the value of \( x \) given the measures of angles \( DBE \) and \( CBE \), we can set up an equation based on the information provided.

Since angle \( DBE \) and angle \( CBE \) are both measured in degrees, we may assume they add up to a straight angle (180 degrees) if they are adjacent angles. Therefore, we have:

\[ (0.3x - 31) + (0.1x - 41) = 180 \]

Now we can combine like terms:

\[ 0.3x + 0.1x - 31 - 41 = 180 \]

\[ 0.4x - 72 = 180 \]

Next, we add 72 to both sides:

\[ 0.4x = 180 + 72 \]

\[ 0.4x = 252 \]

Now, we divide both sides by 0.4 to solve for \( x \):

\[ x = \frac{252}{0.4} \]

\[ x = 630 \]

So, the value of \( x \) is:

\[ \boxed{630} \]