Pregunta
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\( x = 3 \)
Solución
**Step 1: Expand both sides of the equation**
Given the equation:
\[
3(x-2) - 4(x-1) = 2(4-x) - 7
\]
Expand the left-hand side (LHS):
\[
3(x-2) = 3x - 6 \quad \text{and} \quad -4(x-1) = -4x + 4
\]
Thus, the LHS becomes:
\[
3x - 6 - 4x + 4 = -x - 2
\]
Expand the right-hand side (RHS):
\[
2(4-x) = 8 - 2x
\]
Thus, the RHS becomes:
\[
8 - 2x - 7 = 1 - 2x
\]
**Step 2: Set the simplified expressions equal to each other**
The equation now is:
\[
-x - 2 = 1 - 2x
\]
**Step 3: Solve for \( x \)**
Add \( 2x \) to both sides to collect \( x \) terms on one side:
\[
-x + 2x - 2 = 1 - 2x + 2x \quad \Longrightarrow \quad x - 2 = 1
\]
Now, add 2 to both sides:
\[
x - 2 + 2 = 1 + 2 \quad \Longrightarrow \quad x = 3
\]
**Final Answer:**
\[
x = 3
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Beyond the Answer
To solve the equation \( 3(x-2)-4(x-1)=2(4-x)-7 \), let's start by expanding and simplifying both sides. First, expand the left side: \[ 3(x-2) - 4(x-1) = 3x - 6 - 4x + 4 = -x - 2 \] Now expand the right side: \[ 2(4-x) - 7 = 8 - 2x - 7 = -2x + 1 \] Now we can set the simplified expressions equal to each other: \[ -x - 2 = -2x + 1 \] Next, solve for \( x \). Start by adding \( 2x \) to both sides: \[ -x + 2x - 2 = 1 \implies x - 2 = 1 \] Now, add 2 to both sides: \[ x = 3 \] So, the solution to the equation is \( x = 3 \).
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