To solve the equation -3(4x - 5) = 2(1 - 5x) step-by-step without a calculator, follow these steps:
**Step 1: Distribute the coefficients across the parentheses.**
Distribute -3 to each term inside the first set of parentheses: -3 * 4x = -12x and -3 * -5 = 15.
For the second set, distribute 2: 2 * 1 = 2 and 2 * -5x = -10x.
The equation now looks like this:
-12x + 15 = 2 - 10x
**Step 2: Move all terms involving x to one side of the equation.**
To do this, we'll add 12x to both sides of the equation:
-12x + 12x + 15 = 2 - 10x + 12x
This simplifies to:
15 = 2 + 2x
**Step 3: Move the constant terms to the other side.**
Subtract 2 from both sides of the equation:
15 - 2 = 2 + 2x - 2
This simplifies to:
13 = 2x
**Step 4: Solve for x.**
To isolate x, divide both sides by 2:
13 / 2 = 2x / 2
This gives us:
x = 13 / 2 or x = 6.5
So, the value of x that satisfies the given equation is 6.5.