Certainly! Let's solve the equation step-by-step:
Given equation:
[tex]\[ 2(1 + 2x) = 4(x - 2) \][/tex]
1. Distribute the 2 on the left side of the equation:
[tex]\[ 2(1 + 2x) = 2 \cdot 1 + 2 \cdot 2x = 2 + 4x \][/tex]
2. Distribute the 4 on the right side of the equation:
[tex]\[ 4(x - 2) = 4 \cdot x + 4 \cdot (-2) = 4x - 8 \][/tex]
3. Now, set the simplified left side equal to the simplified right side:
[tex]\[ 2 + 4x = 4x - 8 \][/tex]
4. Combine like terms. Subtract \( 4x \) from both sides to start isolating the constant on one side:
[tex]\[ 2 + 4x - 4x = 4x - 8 - 4x \][/tex]
5. This simplifies to:
[tex]\[ 2 = -8 \][/tex]
6. At this point, we observe a contradiction. The statement \( 2 = -8 \) is never true. This means that there is no value of \( x \) that can satisfy the original equation.
Therefore, the equation [tex]\( 2(1 + 2x) = 4(x - 2) \)[/tex] has no solution.
