🧮 algebra

1. **State the problem:** Simplify the expression $$(3.4a - 1.7b) + (2.5a - 3.9b)$$. 2. **Use the distributive property and combine like terms:**

1. **State the problem:** Solve the inequality $$\frac{3}{x} - 5 < 16$$ for $$x$$. 2. **Add 5 to both sides:**

1. **Solve the equation** $y - 12x + 3 = \frac{4}{7}$ for $y$. Start by isolating $y$ on one side:

1. **State the problem:** Solve the equation $$\sqrt{2x - 1} + \sqrt{x - 1} = 5$$ and verify the solutions. 2. **Rewrite the equation:** Let $$a = \sqrt{2x - 1}$$ and $$b = \sqrt{x

1. The problem asks for the domain and range of the function $$f(x) = \sqrt{x + 7} - 2$$. 2. The domain of a square root function $$\sqrt{g(x)}$$ requires the expression inside the

1. The problem asks to identify the graph that shows the inverse of the function $f(x)$, which is an increasing S-shaped curve passing through the origin. 2. The inverse function $

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 6x + 7 = 0$$ using the quadratic formula without simplifying the fraction. 2. **Recall the quadratic formula:** For

1. **Stating the problem:** Reduce the expression $$(3a+b)\cdot(2a-4b)-5a^2$$.

1. The problem is to divide the fraction $\frac{9}{1}$ by the fraction $\frac{7}{6}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times

1. **State the problem:** Solve the equation $$3(2x+1)^2 = 2(52+1)$$ for $x$. 2. **Simplify the right side:** Calculate $52+1$.

1. **State the problem:** Solve the equation $$3(2x+1)^2 = 2(5x+1)$$ for $x$. 2. **Use the formula and rules:** Expand the squared term and simplify both sides.

1. **State the problem:** Graph the parabola given by the equation $$y = -x^2 + 2x + 8$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The equatio

1. **State the problem:** Solve the inequality $$\frac{3x^2}{5} + \frac{x}{4} - (x - 2) - \frac{1}{2}\left(x - \frac{1}{2}\right) \geq \left(\frac{x - 1}{2}\right)^2 + \frac{3x}{5}

1. **State the problem:** We need to graph the quadratic function $$y = 3x^2$$ and understand its properties. 2. **Formula and rules:** The general form of a quadratic function is

1. **State the problem:** Solve the inequality $$\left(-x - \frac{1}{3}\right)^2 + (3x + 1)^2 - \frac{x}{2} + \frac{1}{6} \geq 10x(x - 1) - \frac{37}{9}.$$\n\n2. **Expand the squar

1. **State the problem:** Simplify the expression $$\frac{2x}{x^2 - 3x - 88} - \frac{2x - 1}{x^2 - 10x - 11}$$. 2. **Factor the denominators:**

1. **State the problem:** Solve the inequality $$ (7x - 2)^2 - 7(x - \frac{2}{7})(7x + 1) + \frac{x}{2} > 3(7x - 2) + \frac{1}{7} $$ with the condition $$ x < \frac{2}{7} $$. 2. **

1. **State the problem:** Find the horizontal asymptote, removable and non-removable restrictions, and simplified factored form of the rational function $$y = \frac{x^3 + 4x^2 - 4x

1. The problem is to analyze and understand the graph of the rational function $$y = \frac{3}{x - 4} - 6$$. 2. The general form of a rational function with a vertical asymptote is

1. **State the problem:** Determine which of the given functions are one-to-one functions. 2. **Recall the definition:** A function $f$ is one-to-one (injective) if for every $a$ a

1. **Problem Statement:** Determine which of the given functions are one-to-one functions. 2. **Recall:** A function is one-to-one (injective) if each output corresponds to exactly