Let's go through the details step-by-step of how to solve this equation and combine the like terms.
## Given Equation
The original equation is:
[tex]\[ 3x - 2(x + 3) = 4(x - 2) - 7 \][/tex]
## Step 1: Apply the Distributive Property
First, we need to distribute the terms on both sides of the equation.
### Left Side
[tex]\[ 3x - 2(x + 3) \][/tex]
[tex]\[ = 3x - 2x - 2 \cdot 3 \][/tex]
[tex]\[ = 3x - 2x - 6 \][/tex]
### Right Side
[tex]\[ 4(x - 2) - 7 \][/tex]
[tex]\[ = 4x - 4 \cdot 2 - 7 \][/tex]
[tex]\[ = 4x - 8 - 7 \][/tex]
So, after applying the distributive property, the equation becomes:
[tex]\[ 3x - 2x - 6 = 4x - 8 - 7 \][/tex]
## Step 2: Combine Like Terms
Now, we need to combine the like terms on both sides of the equation.
### On the Left Side
The left side is:
[tex]\[ 3x - 2x - 6 \][/tex]
### On the Right Side
The right side is:
[tex]\[ 4x - 8 - 7 \][/tex]
To combine like terms, Misha should identify terms that are similar and combine them.
### Combining Like Terms
- For the [tex]\(x\)[/tex]-terms on the left side, combine:
[tex]\[ 3x \text{ and } -2x \][/tex]
Thus:
[tex]\[ 3x - 2x \][/tex]
- For the constants on the right side, combine:
[tex]\[ -8 \text{ and } -7 \][/tex]
Thus:
[tex]\[ -8 - 7 \][/tex]
So, the terms Misha should combine are:
[tex]\[ 3x - 2x \][/tex] and [tex]\[ -8 - 7 \][/tex]
Therefore, Misha should combine:
[tex]\[ 3x - 2x \text{ and } -8 - 7. \][/tex]
