🧮 algebra

1. **Stating the problem:** Vi skal løse ligningen $$6x = 4 \cdot (x + 2)$$. 2. **Brug formlen og regler:** Vi starter med at udvide højre side ved at gange 4 med både $$x$$ og 2.

1. **State the problem:** Solve the equation $p + 2p + (p - 2) = 18$ for $p$. 2. **Combine like terms:** Add all the $p$ terms together and simplify the constants.

1. **State the problem:** We have a bouquet with red, purple, and orange balloons. The number of each color is given by: - Red: $2p$

1. **State the problem:** Simplify the complex rational expression \n $$\frac{-\frac{7}{x+7} - \frac{2}{x+6}}{-\frac{6}{x+7}}$$\n

1. **State the problem:** Solve the rational equation $$\frac{2x}{x+5} + \frac{4}{x+3} = \frac{8}{x^2 + 8x + 15}$$. 2. **Factor the denominator on the right:** Note that $$x^2 + 8x

1. **Problem 5:** Determine which set of ordered pairs satisfies the condition that the second number is 2 more than twice the first number. 2. The formula for this condition is:

1. **State the problem:** Solve for $x$ in the equation $$2(x - 2) = 4x - 13$$ and express the answer to the nearest tenth. 2. **Apply the distributive property:** Multiply 2 by ea

1. **State the problem:** Simplify the expression $$\frac{13 + (-3)^2 + 4(-3) + 1 - [-10 - (-6)]}{\left[4 + 5\right] \div \left[4^2 - 3^2(4 - 3) - 8\right] + 12}$$

1. **State the problem:** Solve the equation $X + 3 = 1$ for $X$. 2. **Formula and rules:** To isolate $X$, subtract 3 from both sides of the equation. This uses the rule that you

1. **State the problems:** - Problem 1: Find the value of $$-\frac{1}{2} \times -\frac{1}{3} \times 12$$ in simplest form.

1. **State the problem:** Simplify the expression $$\frac{1}{6} + \frac{1}{3} + 2 \frac{1}{2}$$ to its simplest form. 2. **Convert mixed number to improper fraction:**

1. The problem is to solve the equation $x + 1 = 2x + 2$ for $x$. 2. We use the principle of equality: whatever operation is done on one side must be done on the other side to keep

1. **State the problem:** Simplify and evaluate the expression $$\frac{(3^2)^4}{3 \times 3 \times 3^4}$$. 2. **Recall exponent rules:**

1. The problem asks to find the value of $2^3 \times 2^0$. 2. Recall the rule for multiplying powers with the same base: $a^m \times a^n = a^{m+n}$.

1. **State the problem:** We want to find the sinusoidal function $S(t) = a \cdot \sin(b \cdot t) + d$ modeling the stock price, where $t$ is in radians and $S(t)$ is the stock pri

1. **State the problem:** We want to factorize the expression $$\omega^6 + \omega^5 + \omega^4 + \omega^3 + \omega^2 + \omega + 1$$ where $$\omega$$ is a 7th root of unity, $$\omeg

1. **State the problem:** We are given a complex number $\omega \neq 1$ that satisfies the equation $$z^7 - 1 = 0.$$ We want to factorize the expression $$\omega^6 + \omega^5 + \om

1. **State the problem:** Solve the quadratic equation $2x^2 - 4x = 3$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $$2(3x - 5) + 4 = 3(x + 2) - 1$$. 2. **Use the distributive property:** Multiply terms inside parentheses.

1. **State the problem:** Solve the quadratic equation $$10x^2 - 12x = 0$$ by any method. 2. **Formula and rules:** To solve quadratic equations, one common method is factoring. If

1. Let’s solve it step by step. 🌟 2. Start with $5x + 8 = x - 9$.