Questions: -2(x-4)-3 x<-(4 x+1)+2 x

Transcript text: $-2(x-4)-3 x<-(4 x+1)+2 x$

Solution

Solution Steps

Step 1: Simplify the Inequality

Start with the original inequality: \[ -2(x-4) - 3x < -(4x + 1) + 2x \] Distributing the terms gives: \[ -2x + 8 - 3x < -4x - 1 + 2x \] This simplifies to: \[ 8 - 5x < -2x - 1 \]

Step 2: Rearrange the Inequality

Next, we rearrange the inequality to isolate the variable $x$: \[ 8 + 1 < -2x + 5x \] This simplifies to: \[ 9 < 3x \]

Step 3: Solve for $x$

Now, divide both sides by $3$ to solve for $x$: \[ \frac{9}{3} < x \] This results in: \[ 3 < x \] Thus, the solution set is $x > 3$.

Final Answer

$\boxed{x > 3}$

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