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Solve the linear equation:
[tex]\[ 3.4 + 2(9.7 - 4.8x) = 61.2 \][/tex]

What are the possible steps involved in solving this equation? Check all that apply.

- A. Distribute 2 to 9.7 and [tex]\(-4.8x\)[/tex].
- B. Combine 3.4 and 19.4.
- C. Subtract 3.4 from both sides.
- D. Divide both sides by 22.8.
- E. Subtract 22.8 from both sides.
- F. Divide both sides by [tex]\(-9.6\)[/tex].

Sagot :

GinnyAnsweridn
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
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