Sure, let's solve the equation step-by-step and identify which actions are involved:
Given equation:
[tex]\[ 3.5 + 1.2(6.3 - 7x) = 9.38 \][/tex]
1. Distribute 1.2 to [tex]\( 6.3 \)[/tex] and [tex]\( -7x \)[/tex]:
- When we distribute [tex]\( 1.2 \)[/tex], we get:
[tex]\[ 1.2 \times 6.3 = 7.56 \][/tex]
[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:
- Adding these together:
[tex]\[ 3.5 + 7.56 = 11.06 \][/tex]
So, the equation now is:
[tex]\[ 11.06 - 8.4x = 9.38 \][/tex]
3. Subtract 11.06 from both sides:
- Subtracting [tex]\( 11.06 \)[/tex] from [tex]\( 11.06 \)[/tex] and [tex]\( 9.38 \)[/tex]:
[tex]\[ 11.06 - 11.06 - 8.4x = 9.38 - 11.06 \][/tex]
[tex]\[ -8.4x = -1.68 \][/tex]
Therefore, the three possible steps involved in solving the equation are:
1. Distribute 1.2 to [tex]\( 6.3 \)[/tex] and [tex]\( -7x \)[/tex].
2. Combine 3.5 and 7.56.
3. Subtract 11.06 from both sides.
