Let's solve the given equation step-by-step and see which options are relevant to the solution process.
The equation is:
[tex]\[ 3.5 + 1.2(6.3 - 7x) = 9.38 \][/tex]
1. Distribute 1.2 to 6.3 and -7x:
The first step is to distribute the 1.2 across the terms inside the parenthesis:
[tex]\[ 1.2 \times 6.3 - 1.2 \times 7x \][/tex]
This distributes to:
[tex]\[ 1.2 \times 6.3 = 7.56 \][/tex]
and
[tex]\[ 1.2 \times -7x = -8.4x \][/tex]
So the equation becomes:
[tex]\[ 3.5 + 7.56 - 8.4x = 9.38 \][/tex]
2. Combine 3.5 and 7.56:
Next, combine the constant terms on the left-hand side:
[tex]\[ 3.5 + 7.56 = 11.06 \][/tex]
So the equation is now:
[tex]\[ 11.06 - 8.4x = 9.38 \][/tex]
3. Subtract 11.06 from both sides:
To isolate the term with \( x \), subtract 11.06 from both sides of the equation:
[tex]\[ 11.06 - 8.4x - 11.06 = 9.38 - 11.06 \][/tex]
Simplifying this, we get:
[tex]\[ -8.4x = -1.68 \][/tex]
Thus, the three correct options are:
- Distribute 1.2 to 6.3 and \(-7 x\).
- Combine 3.5 and 7.56.
- Subtract 11.06 from both sides.
