To solve the linear equation:
[tex]\[
3.4 + 2(9.7 - 4.8x) = 61.2
\][/tex]
we can break it down into a series of steps:
1. Distribute 2 to both terms inside the parentheses:
[tex]\[
3.4 + 2 \cdot 9.7 + 2 \cdot (-4.8x)
\][/tex]
This will give us:
[tex]\[
3.4 + 19.4 - 9.6x
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
3.4 + 19.4 - 9.6x \rightarrow 22.8 - 9.6x
\][/tex]
3. Form the new equation and isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
22.8 - 9.6x = 61.2
\][/tex]
4. Subtract 22.8 from both sides:
[tex]\[
-9.6x = 61.2 - 22.8 \rightarrow -9.6x = 38.4
\][/tex]
5. Divide both sides by -9.6:
[tex]\[
x = \frac{38.4}{-9.6} \rightarrow x = -4
\][/tex]
So, in detail, the steps involved in solving the equation are:
- Distribute 2 to 9.7 and [tex]\( -4.8x \)[/tex]
- Combine 3.4 and 19.4
- Subtract 22.8 from both sides
- Divide both sides by -9.6
