First Degree Equations with an Incognita

They are called equal equations in which number and letters (unknowns) appear related by mathematical operations.

An equality between two quantities or expressions

2x - 1 = 5x + 8
2x – 5x = 8 + 1
-3x = 9
X = 9 / -3
X = -3

Problems

Marta is 15 years old, which is one third of her mother's age. How old is Marta's mother?

We call the age of the mother.
The third part of the mother's age is the same as Marta's, that is, 15. Mathematically written:
x / 3 = 15

Subtema

2 – X = X – 8
2 – X + 8 = X
2 + 8 = X + X
10 = 2X
10/2 = X
5 = X

2X - 3 = 53
2X = 53 +3
2X = 56
X = 56/2
X = 28

Equations with Grouping Signs

1) Signs of grouping are deleted
2) The terms are transposed with unknowns and the terms with known values.
3) Similar terms are reduced.
4) The result is simplified to find it Solution.

(5-3x) - (-4x+6) = (8x+11) - (3x-6).
 5-3x+4x-6 = 8x+11-3x+6
 -3x+4x-8x+3x = 11+6-5+6

 -4x = 18

 x = 18/-4

x = – 9/2

5x+{-2x-x+6} = 18-{-7x-6-3x+24}
. 5x-2x-x+6 = 18+7x+6+3x-24
. 5x-2x-x-7x-3x= 18+6-24-6

. -8x = -6

. x = -6/-8

x = 3/4

X-(2X+1) = 8-(3X+3).
• X-2X-1 = 8-3X-3
• X-2X+3X = 8-3+1

• 2X = 6

• X = 6/2

X= 3

Equations with Indicated Products

1. The products indicated in the expression are made.
2.The common terms are transposed (leaving the unknowns to the left and the known values to the right).
3. Similar terms are reduced in each member of the equation.
4. The result is simplified to find the solution.

10(X-9) -9(5-6X) = 2(4X-1) +5(1+2X).
. 10X-90-45+54X = 8X-2+5+10X
. 10X+54X-8X-10X = -2+5+90+45
. 46X = 138
. X = 138/46
X = 3

4x -(2x+3)(3x-5) = 49 -(6x-1)(x-2).
• 4x -(6x^2 -x-15) = 49 -(6x^2 -13x+2)
• 4x-6x^2+x+15 = 49-6x^2+13x-2
• 6x^2-6x^2+4x+x-13x = 49-2-15
• -8x = -32
• x =32/-8
x = -4

x +3(x-1) = 6 -4(2x+3).
 x+3x-3 = 6-8x-12
 x+3x+8x = 6-12+3

 12x= -3

 x = -3/12

x = – 1/4