1) $$ \begin{aligned} 3(x-4)= & 2(-2 x+1) \ 3 x-(1) & =4 x+(2) \ +4 x & +4 x\end{aligned} $$

Question

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3x-1=4x+2$$
- step1: Move the expression to the left side:
  $$3x-4x=2+1$$
- step2: Add and subtract:
  $$-x=2+1$$
- step3: Add and subtract:
  $$-x=3$$
- step4: Change the signs:
  $$x=-3$$
Solve the equation $$ 3(x-4)=2(-2x+1) $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3\left(x-4\right)=2\left(-2x+1\right)$$
- step1: Calculate:
  $$3x-12=2\left(-2x+1\right)$$
- step2: Calculate:
  $$3x-12=-4x+2$$
- step3: Move the expression to the left side:
  $$3x-12-\left(-4x+2\right)=0$$
- step4: Calculate:
  $$7x-14=0$$
- step5: Move the constant to the right side:
  $$7x=0+14$$
- step6: Remove 0:
  $$7x=14$$
- step7: Divide both sides:
  $$\frac{7x}{7}=\frac{14}{7}$$
- step8: Divide the numbers:
  $$x=2$$
Let's solve the equations step by step.

1. **First Equation:**
   $$
   3(x-4) = 2(-2x+1)
   $$
   Expanding both sides:
   $$
   3x - 12 = -4x + 2
   $$
   Now, let's isolate $$x$$:
   $$
   3x + 4x = 2 + 12
   $$
   $$
   7x = 14
   $$
   Dividing both sides by 7:
   $$
   x = 2
   $$

2. **Second Equation:**
   $$
   3x - 1 = 4x + 2
   $$
   Rearranging the equation:
   $$
   3x - 4x = 2 + 1
   $$
   $$
   -x = 3
   $$
   Multiplying both sides by -1:
   $$
   x = -3
   $$

### Summary of Solutions:
- For the first equation, $$ x = 2 $$.
- For the second equation, $$ x = -3 $$.
The solutions are $$ x = 2 $$ and $$ x = -3 $$.

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