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.
