Question 2.3.7: Solve for x: 3x - 4 = - 2x + 6....

Solve for x: 3x – 4 = – 2x + 6.

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To solve the equation, we want to isolate the variable x.

Step 1:

We start by adding 2x to both sides of the equation to eliminate the 2x term on the right side. This gives us 3x + 2x - 4 = -2x + 2x + 6.

Step 2:

Simplifying the equation, we combine like terms on both sides. On the left side, 3x + 2x becomes 5x. On the right side, -2x + 2x cancels out, leaving us with just 6.

Step 3:

To further isolate the variable x, we add 4 to both sides of the equation. This gives us 5x - 4 + 4 = 6 + 4.

Step 4:

By simplifying, the -4 and +4 on the left side cancel out, leaving us with just 5x. On the right side, 6 + 4 equals 10.

Step 5:

To solve for x, we divide both sides of the equation by 5. This gives us (1/5)(5x) = (1/5)(10).

Step 6:

On the left side, the (1/5) and (5x) cancel out, leaving us with just x. On the right side, (1/5)(10) simplifies to 2.

Therefore, the solution to the equation is x = 2.

Final Answer

We begin by adding 2x to both sides:

3x + 2x – 4 = – 2x + 2x + 6 Add 2x to both sides

5x – 4 = 6 Simplify

Now we add 4 to both sides:

$\begin{aligned}5 x-4+ 4 & =6+ 4 & & \text { Add } 4 \text { to both sides } \\5 x & =10 & & \text { Simplify } \\\frac{ 1 }{ 5 }(5 x) & =\frac{ 1 }{ 5 }(10) & & \text { Multiply by } \frac{1}{5} \\x & =2 & & \text { Simplify }\end{aligned}$