🧮 algebra

1. **State the problem:** Simplify the given fractions and check the equality $\frac{8}{12} = \frac{2}{2}$.\n\n2. **Simplify each fraction:**\n- $\frac{3}{5}$ is already in simples

1. **State the problem:** Solve the inequality $$15 - \frac{7x}{5} \geq 9$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 15 from both sides:

1. **State the problem:** Solve the inequality $$18 > 12 - \frac{6}{7}x$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 12 from both sides:

1. **State the problem:** We have a function $f(t)$ graphed and three new functions defined as: - $a(t) = f(t) + 3$

1. **Identify the dependent and independent variables in the first practice problem:** - Problem: The distance $t$ depends on the speed $S$.

1. **State the problem:** Expand and simplify the expression $ (h + 6)(5 - h) $. 2. **Recall the distributive property:** To expand, multiply each term in the first parenthesis by

1. **State the problem:** Solve the quadratic equation $$25z^2 - 30z + 4 = -5$$ using the quadratic formula. 2. **Rewrite the equation:** Move all terms to one side to set the equa

1. **State the problem:** We are given two expressions, $3x - 71$ and $x + 20$, which are labeled near intersections of a diagonal line with two parallel lines. We want to find the

1. **Find the domain of the function** $f(x) = \frac{1}{x - 1}$. 2. The domain of a function is the set of all $x$ values for which the function is defined.

1. **State the problem:** We need to find the sum of the fractions $\frac{1}{8} + \frac{1}{7} + \frac{2}{7} + \frac{7}{8}$. 2. **Formula and rules:** To add fractions, we need a co

1. Let's state the problem: You want to find the possible zeros of a polynomial function. 2. The rule to find possible rational zeros is called the Rational Root Theorem. It says t

1. **State the problem:** Simplify or analyze the polynomial $x^3 + x^2 - 10x + 8$. 2. **Identify the goal:** We can try to factor the polynomial to find its roots or simplify it.

1. The problem is to understand why we only find factors of 8 when factoring the polynomial $x^3 + x^3 - 10x + 8$ using the Rational Root Theorem. 2. The polynomial can be simplifi

1. The problem asks if the first number in the polynomial is 5, would you have to find the factors of 5 and 8 to determine possible zeros. 2. The answer is yes. When using the Rati

1. **State the problem:** We need to find which test point among (2,1), (3,0), (1,2), and (0,0) satisfies the system of inequalities: $$\begin{cases} 10y - 5x \leq 0 \\ 4x + 2y > 1

1. The problem is to graph the function $$y = 4 + \sqrt{x}$$. 2. Important note: The square root function $$\sqrt{x}$$ is only defined for $$x \geq 0$$, so the domain of this funct

1. Let's state the problem: We want to find the factors of the polynomial $$x^3 + x^2 - 10x + 8$$. 2. The Rational Root Theorem tells us that any rational root of a polynomial with

1. The problem is to understand and analyze the function $y = 4\sqrt{x}$.\n\n2. This function represents $y$ as four times the square root of $x$. The square root function $\sqrt{x

1. **State the problem:** Factor the polynomial $$P(x) = 3x^4 + x^3 - 14x^2 - 4x + 8$$ completely. 2. **List possible rational zeros:** By the Rational Root Theorem, possible zeros

1. **State the problem:** Simplify the expression $v - \frac{v}{3}$. 2. **Write the expression with a common denominator:** To combine the terms, express $v$ as $\frac{3v}{3}$.

1. **State the problem:** Simplify the algebraic expression $$\frac{x}{4} + \frac{2y}{3} - \frac{5y}{6} + \frac{4x}{3}$$. 2. **Group like terms:** Group the terms with $x$ and the