Factorize x2 + 3x + 2, solve (x+1)(x+2) for x=6, check 5x gtr 2y for x=6, y=2, and solve 5q+25 gtr 10 by…

Question

Factorize x2 + 3x + 2, solve (x+1)(x+2) for x=6, check 5x gtr 2y for x=6, y=2, and solve 5q+25 gtr 10 by dividing by −5.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your assignment questions:

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

Find two numbers that multiply to 2 and add to 3.
The numbers are 1 and 2.
Rewrite the middle term using these numbers.
$x^2 + x + 2x + 2$
Factor by grouping.
$x(x+1) + 2(x+1)$
Factor out the common term $(x+1)$ .
$(x+1)(x+2)$
The factored expression is $\boxed{(x+1)(x+2)}$ .

2) Solve the equation $(x+1)(x+2)$ where $x=6$

This is an expression to evaluate, not an equation to solve for $x$ .
Substitute $x=6$ into the expression.
$(6+1)(6+2)$
Perform the additions inside the parentheses.
$(7)(8)$
Multiply the numbers.
$56$
The value of the expression is $\boxed{56}$ .

3) Solve for $x$ $5x \ge 2y$ where $x=6$ , $y=2$

This question asks to check if the inequality holds true for the given values of $x$ and $y$ .
Substitute $x=6$ and $y=2$ into the inequality.
$5(6) \ge 2(2)$
Perform the multiplications.
$30 \ge 4$
Check if the inequality is true.
30 is indeed greater than or equal to 4.
The inequality is $\boxed{True}$ .

4) Solve for $q$ by dividing the equation $5q + 25 \le 10$ by $-5$
Divide all terms in the inequality by $-5$ .
Remember to reverse the inequality sign when dividing by a negative number.
$\frac{5q}{-5} + \frac{25}{-5} \ge \frac{10}{-5}$
Simplify each term.
$-q - 5 \ge -2$
Add 5 to both sides of the inequality.
$-q \ge -2 + 5$ $-q \ge 3$
Multiply both sides by $-1$ to solve for $q$ .
Remember to reverse the inequality sign again.
$q \le -3$
The solution for $q$ is $\boxed{q \le -3}$ .

Factorize x2 + 3x + 2, solve (x+1)(x+2) for x=6, check 5x gtr 2y for x=6, y=2, and solve 5q+25 gtr 10 by dividing by -5.