🧮 algebra

1. **State the problem:** Solve the equation $$3|x - 5| = 12$$ for $$x$$. 2. **Isolate the absolute value:** Divide both sides by 3 to get $$|x - 5| = \frac{12}{3}$$.

1. The problem is to solve the equation $|x| = 2$. 2. Recall that the absolute value $|x|$ represents the distance of $x$ from zero on the number line, so $|x| = a$ means $x = a$ o

1. **State the problem:** Factor the trinomial $$x^2 + 7x + 12$$. 2. **Formula and rules:** To factor a trinomial of the form $$x^2 + bx + c$$, find two numbers that multiply to $$

1. The problem involves understanding the relationships between variables $b$ and $m$ given by three equations and their corresponding tables and graphs. 2. The first equation is $

1. The problem asks for an expression representing the distance a fish swims in $x$ hours, given its speed is 12 miles per hour. 2. The formula for distance when speed and time are

1. **State the problem:** Solve the system of equations by substitution: $$y = -x$$

1. **State the problem:** Solve the system of equations by substitution: $$y = -4x$$

1. **State the problem:** Simplify the expression $$\frac{3x}{x-2} \times \frac{x}{2x+4} \times \frac{5}{x}$$. 2. **Recall the rules:** When multiplying fractions, multiply the num

1. **State the problem:** Simplify the expression $$\frac{x}{x^2-1} - \frac{x-3}{x-1}$$. 2. **Recall the formula and rules:** The denominator $x^2-1$ can be factored using the diff

1. **State the problem:** Simplify the expression $$\frac{x}{x^{2-1}} - \frac{x-3}{x-1}$$. 2. **Rewrite the powers:** Note that $$x^{2-1} = x^1 = x$$, so the first fraction becomes

1. **State the problem:** Simplify the expression $$\frac{x}{x^2-1} - \frac{x-3}{x-1}$$. 2. **Recall the formula and rules:**

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominators involving $x

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominators involving $x

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominator involving $x$

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** The denominators are $x$, $6x$, and $2x$

1. **State the problem:** Simplify the rational expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominators inv

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** All terms have denominator involving $x$

1. **State the problem:** Simplify the expression $$\frac{3x+4}{x} - \frac{5}{6x} + \frac{9}{2x}$$. 2. **Identify the common denominator:** The denominators are $x$, $6x$, and $2x$

1. State the problem: Simplify $\sqrt[3]{\frac{49}{27}}\, j^{1/3}$. 2. Use the cube root rule:

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{49}{27}} \cdot j^{\frac{1}{3}}$$ where $j$ is a variable. 2. **Recall the cube root and exponent rules:**

### Problem\nSolve for $a$ in the equation $a^3+a^2=36$.\n\n1. Start with the given equation\n$$a^3+a^2=36$$\n\n2. Move everything to one side\n$$a^3+a^2-36=0$$\n\n3. Factor the cu