Let's solve the linear equation step by step.
Given equation:
[tex]\[ 3.4 + 2(9.7 - 4.8x) = 61.2 \][/tex]
1. Distribute 2 to [tex]\(9.7\)[/tex] and [tex]\(-4.8x\)[/tex]:
[tex]\[ 3.4 + 2 \cdot 9.7 - 2 \cdot 4.8x = 61.2 \][/tex]
[tex]\[ 3.4 + 19.4 - 9.6x = 61.2 \][/tex]
2. Combine [tex]\(3.4\)[/tex] and [tex]\(19.4\)[/tex]:
[tex]\[ 22.8 - 9.6x = 61.2 \][/tex]
3. Subtract [tex]\(22.8\)[/tex] from both sides:
[tex]\[ 22.8 - 9.6x - 22.8 = 61.2 - 22.8 \][/tex]
[tex]\[ -9.6x = 38.4 \][/tex]
4. Divide both sides by [tex]\(-9.6\)[/tex]:
[tex]\[ x = \frac{38.4}{-9.6} \][/tex]
[tex]\[ x = -4 \][/tex]
From these steps, the items to check are:
- Distribute 2 to 9.7 and [tex]\( -4.8x \)[/tex]: This is correct and necessary.
- Combine 3.4 and 19.4: This is correct and necessary.
- Subtract 22.8 from both sides: This is correct and necessary.
- Divide both sides by -9.6: This is correct and necessary.
Items to avoid:
- Add 3.4 and 2: This step would be incorrect because we need to follow the correct order of operations (distribute before combining).
- Divide both sides by 22.8: This step does not apply to solving this equation.
So, the possible steps involved in solving this 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.
