Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
There is no solution to the equation.
Solution
1. Start with the given equation:
\[
2(x+1)-(3-2x)=2x-(7-2x)
\]
2. Expand the expressions on both sides:
- Left-hand side:
\[
2(x+1)=2x+2
\]
Thus,
\[
2x+2 - (3-2x)=2x+2-3+2x=4x-1
\]
- Right-hand side:
\[
2x-(7-2x)=2x-7+2x=4x-7
\]
3. The equation now simplifies to:
\[
4x-1=4x-7
\]
4. Subtract \(4x\) from both sides:
\[
4x-1-4x=4x-7-4x \quad \Longrightarrow \quad -1=-7
\]
5. The statement \(-1=-7\) is a contradiction, which means there is no value of \(x\) that satisfies the original equation.
\[
\textbf{Answer: No solution.}
\]
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Simplify this solution The Deep Dive
To solve the equation \( 2(x+1)-(3-2 x)=2 x-(7-2 x) \), first, simplify both sides. On the left side, distribute to get: \[ 2x + 2 - 3 + 2x = 4x - 1 \] On the right side: \[ 2x + 2x - 7 = 4x - 7 \] Now, set the simplified sides equal: \[ 4x - 1 = 4x - 7 \] Next, subtract \( 4x \) from both sides: \[ -1 = -7 \] This is a contradiction, meaning there are no values for \( x \) that satisfy the equation. Therefore, the solution is that the equation has no solution!
