1.### What is the solution to x + 5 = 12?

Answer:
7

Explanation:

The solution to the equation x + 5 = 12 is:

Subtract 5 from both sides to isolate x:

x + 5 - 5 = 12 - 5

x = 7

So, x = 7.

Subtract 5 from both sides to isolate x:

x + 5 - 5 = 12 - 5

x = 7

So, x = 7.

2.### How do you simplify 3x + 2x?

Answer:
5x

Explanation:

Combine like terms: Both terms have the same variable x, so you can add their coefficients (3 and 2).

Add the coefficients: 3 + 2 = 5.

Rewrite the expression: 5x.

So, 3x + 2x simplifies to 5x.

Add the coefficients: 3 + 2 = 5.

Rewrite the expression: 5x.

So, 3x + 2x simplifies to 5x.

3.### What is the product of (x - 3)(x + 3)?

Answer:
X^2 - 9

Explanation:

To find the product of (x - 3)(x + 3), you can use a special algebraic formula called the difference of squares. The difference of squares formula states that:

(a - b)(a + b) = a^2 - b^2

In this expression, "a" is x, and "b" is 3. So when you apply the formula:

(x - 3)(x + 3) becomes x^2 - 3^2.

Next, calculate the square of 3:

3^2 = 9.

So, the expression simplifies to:

x^2 - 9.

Therefore, the product of (x - 3)(x + 3) is x^2 - 9.

(a - b)(a + b) = a^2 - b^2

In this expression, "a" is x, and "b" is 3. So when you apply the formula:

(x - 3)(x + 3) becomes x^2 - 3^2.

Next, calculate the square of 3:

3^2 = 9.

So, the expression simplifies to:

x^2 - 9.

Therefore, the product of (x - 3)(x + 3) is x^2 - 9.

4.### What is the result of (2x)^2?

Answer:
4x^2

Explanation:

To calculate the result of (2x)^2, you need to square both the coefficient (2) and the variable (x):

First, square the coefficient 2:

2^2 = 4.

Then, square the variable x:

x^2 = x^2.

Combine the results:

4x^2.

So, when you square (2x), the result is 4x^2.

First, square the coefficient 2:

2^2 = 4.

Then, square the variable x:

x^2 = x^2.

Combine the results:

4x^2.

So, when you square (2x), the result is 4x^2.

5.### Which expression is equivalent to 4(x + 2)?

Answer:
4x + 8

Explanation:

The expression that is equivalent to 4(x + 2) is 4x + 8.

This is found by distributing the 4 to both terms inside the parentheses:

4(x + 2) = 4 * x + 4 * 2 = 4x + 8.

This is found by distributing the 4 to both terms inside the parentheses:

4(x + 2) = 4 * x + 4 * 2 = 4x + 8.

6.### What is the value of x if 3x - 2 = 7?

Answer:
3

Explanation:

To find the value of x in the equation 3x - 2 = 7, follow these steps:

Add 2 to both sides of the equation to isolate the term with x:

3x - 2 + 2 = 7 + 2

This simplifies to:

3x = 9

Divide both sides by 3 to solve for x:

3x / 3 = 9 / 3

This simplifies to:

x = 3

So, the value of x is 3.

Add 2 to both sides of the equation to isolate the term with x:

3x - 2 + 2 = 7 + 2

This simplifies to:

3x = 9

Divide both sides by 3 to solve for x:

3x / 3 = 9 / 3

This simplifies to:

x = 3

So, the value of x is 3.

7.### Solve for x: 2x/3 = 8

Answer:
12

Explanation:

To solve for x in the equation 2x/3 = 8:

Multiply both sides by 3:

2x = 8 * 3

2x = 24

Divide both sides by 2:

x = 24 / 2

x = 12

So, x = 12.

Multiply both sides by 3:

2x = 8 * 3

2x = 24

Divide both sides by 2:

x = 24 / 2

x = 12

So, x = 12.

8.### What is the quadratic formula?

Answer:
(-b±√(b^2-4ac))/2a

Explanation:

The quadratic formula (-b±sqrt(b^2-4ac))/2a is derived from rearranging the standard form of a quadratic equation ax^2 + bx + c = 0. It provides a systematic method for finding the roots of any quadratic equation, crucial for solving quadratic equations where factors are not easily apparent.

9.### If y varies directly with x, and y = 6 when x = 2, what is y when x = 3?

Answer:
9

Explanation:

If y varies directly with x, the relationship can be written as:

y = kx

where k is the constant of proportionality.

Given that y = 6 when x = 2, you can find k:

6 = k(2)

k = 6/2 = 3

Now that you know k = 3, you can find y when x = 3:

y = 3(3) = 9

So, y = 9 when x = 3.

y = kx

where k is the constant of proportionality.

Given that y = 6 when x = 2, you can find k:

6 = k(2)

k = 6/2 = 3

Now that you know k = 3, you can find y when x = 3:

y = 3(3) = 9

So, y = 9 when x = 3.

10.### What is the simplified form of (x^2 - 4)/(x - 2)?

Answer:
X + 2

Explanation:

To simplify the expression (x^2 - 4)/(x - 2):

Factor the numerator. The expression x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2).

The expression now looks like this: (x - 2)(x + 2)/(x - 2).

Since (x - 2) appears in both the numerator and the denominator, you can cancel it out, leaving you with just x + 2.

So, the simplified form of (x^2 - 4)/(x - 2) is x + 2, with the condition that x ≠ 2, because division by zero is undefined.

Factor the numerator. The expression x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2).

The expression now looks like this: (x - 2)(x + 2)/(x - 2).

Since (x - 2) appears in both the numerator and the denominator, you can cancel it out, leaving you with just x + 2.

So, the simplified form of (x^2 - 4)/(x - 2) is x + 2, with the condition that x ≠ 2, because division by zero is undefined.

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