Answer :
Certainly! Let's solve the equation step by step:
Given equation:
[tex]\[ 3(x + 2) = 2(2 - x) \][/tex]
1. Distribute the coefficients to the terms inside the parentheses:
[tex]\[ 3 \cdot (x + 2) = 3x + 6 \][/tex]
[tex]\[ 2 \cdot (2 - x) = 4 - 2x \][/tex]
So, the equation becomes:
[tex]\[ 3x + 6 = 4 - 2x \][/tex]
2. Move all the terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side to solve for [tex]\( x \)[/tex]:
[tex]\[ 3x + 6 + 2x = 4 - 2x + 2x \][/tex]
Simplify both sides:
[tex]\[ 5x + 6 = 4 \][/tex]
3. Isolate the term with [tex]\( x \)[/tex] by subtracting 6 from both sides:
[tex]\[ 5x = 4 - 6 \][/tex]
Simplify the right-hand side:
[tex]\[ 5x = -2 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ x = \frac{-2}{5} \][/tex]
Therefore, the solution is:
[tex]\[ x = -\frac{2}{5} \][/tex]
Hence, the correct answer is:
B. [tex]\( x = -\frac{2}{5} \)[/tex]
Given equation:
[tex]\[ 3(x + 2) = 2(2 - x) \][/tex]
1. Distribute the coefficients to the terms inside the parentheses:
[tex]\[ 3 \cdot (x + 2) = 3x + 6 \][/tex]
[tex]\[ 2 \cdot (2 - x) = 4 - 2x \][/tex]
So, the equation becomes:
[tex]\[ 3x + 6 = 4 - 2x \][/tex]
2. Move all the terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side to solve for [tex]\( x \)[/tex]:
[tex]\[ 3x + 6 + 2x = 4 - 2x + 2x \][/tex]
Simplify both sides:
[tex]\[ 5x + 6 = 4 \][/tex]
3. Isolate the term with [tex]\( x \)[/tex] by subtracting 6 from both sides:
[tex]\[ 5x = 4 - 6 \][/tex]
Simplify the right-hand side:
[tex]\[ 5x = -2 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ x = \frac{-2}{5} \][/tex]
Therefore, the solution is:
[tex]\[ x = -\frac{2}{5} \][/tex]
Hence, the correct answer is:
B. [tex]\( x = -\frac{2}{5} \)[/tex]
