Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Question

ScanSolve AI Tutor · Accepted Answer

Here are the step-by-step solutions for the problems.

1. Factorize $x^2 + 3x + 2$

Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).
The numbers are 1 and 2, because $1 \times 2 = 2$ and $1 + 2 = 3$ .
Write the quadratic expression in factored form using these numbers.
$x^2 + 3x + 2 = (x + 1)(x + 2)$
The factored form is $\boxed{(x + 1)(x + 2)}$ .

2. Solve the equation $(x+1)(x+2)$

Assuming the equation is $(x+1)(x+2) = 0$ , as is standard for "solve the equation" when given factors.
Set each factor equal to zero.
For a product of factors to be zero, at least one of the factors must be zero.
$x + 1 = 0 \quad \text{or} \quad x + 2 = 0$
Solve each linear equation for x.
$x + 1 = 0 \implies x = -1$ $x + 2 = 0 \implies x = -2$
The solutions are $\boxed{x = -1, x = -2}$ .

3. Solve for x: $5x \ge 2y$ Where $x=6, y=2$

This question asks to "solve for x" but then provides a specific value for x. We will first solve the inequality for x in terms of y, and then verify if the given values satisfy the inequality.
Solve the inequality for x.
$5x \ge 2y$
Divide both sides by 5:
$x \ge \frac{2y}{5}$
Substitute the given values $x=6$ and $y=2$ into the original inequality to verify.
$5(6) \ge 2(2)$ $30 \ge 4$
This statement is true.
The solution for x in terms of y is $\boxed{x \ge \frac{2y}{5}}$ . The given values $x=6, y=2$ satisfy the inequality.

4. Solve for a by dividing the equation $5a + 25 \le 10$ by -5
Write down the inequality.
$5a + 25 \le 10$
Divide every term in the inequality by -5.
Remember to reverse the inequality sign when dividing by a negative number.
$\frac{5a}{-5} + \frac{25}{-5} \ge \frac{10}{-5}$ $-a - 5 \ge -2$
Isolate the term with 'a' by adding 5 to both sides.
$-a \ge -2 + 5$ $-a \ge 3$
Multiply both sides by -1 to solve for 'a'.
Remember to reverse the inequality sign again.
$(-1)(-a) \le (-1)(3)$ $a \le -3$
The solution is $\boxed{a \le -3}$ .

Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Step-by-step solution

Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Write the quadratic expression in factored form using these numbers.

Set each factor equal to zero.

Solve each linear equation for x.

Solve the inequality for x.

Substitute the given values $x=6$ and $y=2$ into the original inequality to verify.

Write down the inequality.

Divide every term in the inequality by -5.

Isolate the term with 'a' by adding 5 to both sides.

Multiply both sides by -1 to solve for 'a'.

Still stuck on this one?

More Mathematics Questions

Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Step-by-step solution

Find two numbers that multiply to the constant term (2) and add up to the coefficient of the middle term (3).

Write the quadratic expression in factored form using these numbers.

Set each factor equal to zero.

Solve each linear equation for x.

Solve the inequality for x.

Substitute the given values x=6x=6x=6 and y=2y=2y=2 into the original inequality to verify.

Write down the inequality.

Divide every term in the inequality by -5.

Isolate the term with 'a' by adding 5 to both sides.

Multiply both sides by -1 to solve for 'a'.

Still stuck on this one?

More Mathematics Questions

Substitute the given values $x=6$ and $y=2$ into the original inequality to verify.