In the video, the instructor, Marca, demonstrates how to solve a first-degree equation requested by a student. The equation involves simplifying terms and applying distributive properties to isolate the variable 'x'. The solution process includes eliminating parentheses, combining like terms, and ultimately dividing both sides of the equation by a coefficient to find the value of 'x'. The final answer is presented in both fractional (5/4) and decimal (1.25) forms.
Here are the key facts from the text, without opinions and with each fact numbered and in a short sentence:
1. The equation to be solved is 3 - 3x - 6 = 2x + (4 - x).
2. The equation is a first-degree equation because the x is taken to the power of one.
3. To eliminate the parentheses, multiply the minus one by the terms inside the parentheses.
4. Multiplying minus one by minus six results in plus six.
5. The distributive property is used to multiply the minus one by the terms inside the parentheses.
6. After distributing, the equation becomes -3x - 6 = 2x + 4 - x.
7. Combining like terms, the equation becomes -3x - 6 = x + 4.
8. To isolate the variable x, move all terms with x to one side of the equation and all constant terms to the other side.
9. Adding 3x to both sides of the equation results in -6 = 4x + 4.
10. Subtracting 4 from both sides of the equation results in -10 = 4x.
11. Dividing both sides of the equation by 4 results in -10/4 = x.
12. Simplifying the fraction, -10/4 = -5/2.
13. To write the answer in decimal form, divide the numerator by the denominator: -5/2 = -2.5.
14. The value of x is -2.5.
Note: Some of the facts may seem redundant or trivial, but I've tried to extract every relevant piece of information from the text.