Category: Algebra

THIS QUESTION COMING IN NDA

tengo trabajos de algebra de 3er grado de secundaria por si pueden servir, solo necesitaria saber el tema que se esta viendo para poder compartirlo

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Question 1Ani is 4 years older than Budi. The sum of their ages now is 20. Suppose Budi's age is x.Question:How old are Ani and Budi now?

Saya masih bingung cara menyelesaikan persamaan aljabar sederhana.

Tolong jelaskan langkah-langkahnya dengan mudah dipahamiContoh soal:

2x + 5 = 15 bagaimana cara mencari nilai x

What is x + y = 2 ?

The equation x + y = 2 means that the sum of x and y equals 2.

There isnt just one answerthere are infinitely many pairs of numbers that satisfy it. For example:

• x = 0, y = 2
• x = 1, y = 1
• x = 2, y = 0
• x = -1, y = 3
• x = 4, y = -2

All of these work because when you add x + y, the result is 2.

You can also write one variable in terms of the other:

• y = 2 x
  or
• x = 2 y

This is a linear equation, and if you graph it, it forms a straight line.

If you want, I can also:

• Show the graph, or
• Explain how to solve it step-by-step.

Because it has continuous values, so it stops for only three digits and as it is also irrational and infinite

1. x+y+z = 3

2. x^2+y^2+z^2 = 3

3. x^3+y^3+z^3 = 3

question

a. Find a simple set of integer values for (x,y,z)

that satisfies all three equations.

An algebraic expression is a mathematical phrase made up of numbers, variables (letters), and operations such as addition (+), subtraction (), multiplication (), or division (). It represents a value but does not have an equal sign.

For example, 3x + 5 is an algebraic expression where 3 is a coefficient, x is a variable, and + 5 is a constant. Algebraic expressions are used to represent unknown values and to describe relationships in mathematics.

1. When a = 1 (Easy Case)

Example:
$x^2+7x+10$x2+7x+10

Use this idea: Find two numbers that multiply to $c$c and add to $b$b.

Here:

• Multiply to 10
• Add to 7

Numbers: 5 and 2

So the factorization is:

$(x+5)(x+2)$(x+5)(x+2)

Check:
5 2 = 10
5 + 2 = 7

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2. When a 1 (AC Method)

Example:
$2x^2+7x+3$2x2+7x+3

Step 1: Multiply a c

2 3 = 6

Step 2: Find two numbers

• Multiply to 6
• Add to 7

Numbers: 6 and 1

Step 3: Rewrite the middle term

$2x^2+6x+x+3$2x2+6x+x+3

Step 4: Factor by grouping

$(2x^2+6x)+(x+3)$(2x2+6x)+(x+3)

Factor each group:

$2x(x+3)+1(x+3)$2x(x+3)+1(x+3)

Step 5: Final factor

$(2x+1)(x+3)$(2x+1)(x+3)

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3. Quick Pattern Method (for $x^2+bx+c$x2+bx+c)

If the first term is $x^2$x2, you can use this shortcut:

$x^2+bx+c=(x+\_)(x+\_)$x2+bx+c=(x+_)(x+_)

Just find numbers that:

• Multiply = c
• Add = b

Example:

$x^2+9x+20$x2+9x+20

Numbers that multiply to 20 and add to 9:

4 and 5

$(x+4)(x+5)$(x+4)(x+5)

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4. Always Check Your Answer

Multiply the factors again (FOIL method).

Example:

$(x+4)(x+5)$(x+4)(x+5)

FOIL:

• First: $x^2$x2
• Outer: $5x$5x
• Inner: $4x$4x
• Last: $20$20

$x^2+9x+20$x2+9x+20

Correct

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5. Tips to Factor Faster

Look for common factors first
Example:

$2x^2+10x+12$2x2+10x+12

Factor 2 first:

$2(x^2+5x+6)$2(x2+5x+6)

Then factor inside:

$2(x+2)(x+3)$2(x+2)(x+3)

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Memorize multiplication pairs

Example:

12 (1,12) (2,6) (3,4)
20 (1,20) (2,10) (4,5)

This makes factoring much faster.

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Example Practice

1. $x^2+8x+15$x2+8x+15

Numbers: 3 and 5

$(x+3)(x+5)$(x+3)(x+5)

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1. $x^2+11x+24$x2+11x+24

Numbers: 3 and 8

$(x+3)(x+8)$(x+3)(x+8)

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1. $3x^2+10x+3$3x2+10x+3

Multiply a c

3 3 = 9

Numbers: 9 and 1

Final:

$(3x+1)(x+3)$(3x+1)(x+3)