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Bianca wrote the steps for her solution to the equation [tex]$2.3 + 8(1.3x - 4.75) = 629.9$[/tex]. She left out the description for the last step.

Bianca's Solution
\begin{tabular}{|c|l|c|}
\hline
& \multicolumn{1}{|c|}{Steps} & Resulting Equations \\
\hline
1 & Use the distributive property to simplify. & [tex]$2.3 + 10.4x - 38 = 629.9$[/tex] \\
\hline
2 & Combine like terms. & [tex]$10.4x - 35.7 = 629.9$[/tex] \\
\hline
3 & Use the addition property of equality. & [tex]$10.4x = 665.6$[/tex] \\
\hline
4 & & [tex]$x = 64$[/tex] \\
\hline
\end{tabular}

What is the missing step of her solution?

A. Add 10.4 to both sides.

B. Add negative 10.4 to both sides.

C. Divide both sides by 10.4.



Answer :

GinnyAnswer
Let's go through the steps of solving the equation [tex]\( 2.3 + 8(1.3x - 4.75) = 629.9 \)[/tex] in detail:

1. Use the distributive property to simplify:

We start by distributing the 8 to both [tex]\( 1.3x \)[/tex] and [tex]\(-4.75\)[/tex]:

[tex]\[ 2.3 + 8(1.3x - 4.75) = 2.3 + 10.4x - 38 \][/tex]

2. Combine like terms:

Now, we combine the constant terms [tex]\( 2.3 \)[/tex] and [tex]\(-38\)[/tex]:

[tex]\[ 2.3 + 10.4x - 38 = 10.4x - 35.7 \][/tex]

So the equation becomes:

[tex]\[ 10.4x - 35.7 = 629.9 \][/tex]

3. Use the addition property of equality:

To isolate the term with [tex]\( x \)[/tex], we add 35.7 to both sides of the equation:

[tex]\[ 10.4x - 35.7 + 35.7 = 629.9 + 35.7 \][/tex]

Simplifying, we get:

[tex]\[ 10.4x = 665.6 \][/tex]

4. Divide both sides by 10.4:

The missing step involves dividing both sides of the equation by 10.4 to solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{665.6}{10.4} \][/tex]

Simplifying this gives:

[tex]\[ x = 64 \][/tex]

So, the missing step in her solution is: Divide both sides by 10.4.

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