🧮 algebra

1. **State the problem:** Solve the inequality $$6(2x+1) - 8 > 5(1+2x) - 9$$. 2. **Apply the distributive property:**

1. We are asked to solve the inequality $$4(8 - x) \geq 3(3x - 20) - 25$$. 2. First, expand both sides using the distributive property:

1. **Stating the problem:** We have three sets of problems involving functions and points:

1. **State the problem:** Solve the inequality $3x^2 - x - 2 > 0$. 2. **Find the roots of the quadratic equation:** To understand where the parabola is above zero, first solve $3x^

1. نبدأ ببيان المسألة: لدينا دالة $m$ معرفة بالعلاقة $$m = w + (m - w) (f_1, f_2)$$ حيث $f_1 = 1$ و $f_2 = 0$. 2. نعلم أن $m$ يمكن كتابتها على شكل متعدد حدود من الدرجة الثانية: $$m

1. **State the problem:** Simplify the expression $$\frac{(2u^{2}v^{3}w^{3})(5u^{3}v^{4}w^{2})}{\frac{-2x^{3}y^{2}z}{6x^{2}y^{3}z^{6}}} \quad \text{and} \quad \frac{(3s^{11})(9s^{-

1. Stating the problem: Calculate the value of the expression $$56.403 + 0.000149(1724.4) - 0.0000593(63.51) + 0.163(35) + 0.873(0)$$. 2. Perform each multiplication:

1. **State the problem:** Find $x$ if $\log_3(2x + 5) = 5$. 2. **Recall the logarithm definition:** $\log_b(a) = c$ means $b^c = a$.

1. **State the problem:** Simplify and solve the equation $$\frac{3}{x+5} - \frac{1}{x^2 + 2x - 15} = \frac{1}{x+5}$$. 2. **Factor the quadratic denominator:** Note that $$x^2 + 2x

1. **State the problem:** Simplify and solve the equation $$\frac{3}{x+5} - \frac{1}{x^2 + 2x - 15} = \frac{1}{x+5}$$. 2. **Factor the quadratic denominator:** Note that $$x^2 + 2x

1. The problem is to find the sum of integers from 1 to $n$. 2. The formula to find the sum of the first $n$ integers is given by the arithmetic series sum formula:

1. **State the problem:** Evaluate the expression $$[(-3)(4) + 5(-3)][4(-5) - 5(-3)]^2$$. 2. **Apply multiplication inside the brackets:**

1. The problem is to graph the function $y = x^2 - 2x + 1$ and understand its shape. 2. The function is a quadratic polynomial, which graphs as a parabola. The general form is $y =

1. **Problem statement:** Simplify the expression $$9x - (3 - 3x)$$ by first removing the parentheses and then combining like terms. 2. **Formula and rules:** When removing parenth

1. **Problem Statement:** Find the value of $n$ for the expression $$\frac{(n+2)!}{(n-1)!}.$$ 2. **Recall the factorial definition:**

1. **Problem Statement:** Evaluate $$\frac{(n+2)!}{(n-1)!}$$ for a general $n$. 2. **Recall the factorial definition:**

1. **State the problem:** Evaluate the expression $$\frac{x^2 - 4x + 2}{x}$$ at $$x = 4$$. 2. **Write the expression:** $$\frac{x^2 - 4x + 2}{x}$$.

1. **State the problem:** Simplify the expression $$(2x^2 + yx^2)(3x^2 + 3x^2).$$ 2. **Combine like terms inside the parentheses:**

1. **Problem Statement:** Find the value of $n$ if $$\frac{n!}{(n-3)!} = 990.$$

1. **State the problem:** Factorize the polynomial $x^4 - 13x^2 - 36$. 2. **Identify the type of polynomial:** This is a quartic polynomial in terms of $x$, but notice it can be tr

1. **State the problem:** Factor the polynomial $$x^4 + 6x^3 + 16x^2 + 18x + 7$$. 2. **Recall the formula and rules:** To factor a quartic polynomial, try to express it as a produc