FIRST-DEGREE EQUATIONS WITH AN INCOGNITE - Coggle Diagram
FIRST-DEGREE EQUATIONS WITH AN INCOGNITE
An equation is an equality between two quantities or expressions. For example: a = b; a + b = c; (ad - b) ÷ e = f.
An equation with an unknown is one that only has one letter (unknown quantity because we do not yet know how much it is worth, unlike numbers); it does not matter how many times the letter is repeated as long as it is only the same letter.
An equation with an unknown is of the first degree when the greatest exponent of that unknown is one (1). If the greatest exponent were two (2) then the equation would be of the second degree, and so on.
SOLVING EQUATIONS WITH GROUPING SIGNS
To solve this type of equations, we must first suppress the grouping signs considering the law of signs, and if there are several groupings, we develop the operations from the inside out.
2x - [x - (x -50)] = x - (800 -3x)
2x - [x -x +50] = x -800 + 3x First we remove the parentheses.
2x -  = 4x -800 We reduce like terms.
2x -50 = 4x -800 Now we remove the brackets.
2x -4x = -800 +50 We transpose the terms, using the criterion of inverse operations.
-2x = -750 Again we reduce like terms
x = -750 / -2 = 375 We solve for x, dividing to -2, then we simplify.
RESOLUTION OF EQUATIONS WITH INDICATED PRODUCTS
To solve this type of equations, first the indicated products are carried out and then the general procedure is followed (applying the criterion of inverse operations).
5 (x -3) - (x -1) = (x +3) -10
5x -15 -x -1 = x +3 -10 We solve the indicated product, and additionally we eliminate the parentheses.
5x -x -x = 3 -10 +15 We take the like terms to one side of the equality, and the independent terms to the other side (we use inverse operations.)
3x = 9 We reduce like terms on both sides of the equality.
x = 9/3 = 3 We solve for x passing 3 to divide, then we simplify.
To solve a problem, we must pose it mathematically and then perform the corresponding operations to find the value of the unknown (the data we want to know).