🧮 algebra

1. **State the problem:** We are given two functions: $$F(x) = 6 + |-2x| - x^2$$

1. **State the problem:** Solve the equation $$0 = 3 (x - 2)^2 + 4$$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** We need to solve the expression $4^2(-4-4)(-4+1)$. 2. **Recall the order of operations:** Calculate powers first, then evaluate expressions inside parenth

1. **State the problem:** Solve the expression $-4^2(-4-4)(-4+1)$. 2. **Recall order of operations:** Exponents are evaluated before multiplication and subtraction inside parenthes

1. **State the problem:** Solve the quadratic equation $x^2 - 5x + 1 = 0$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$:

1. **State the problem:** Solve the inequality $$\frac{1}{2}(3x - 4) \leq \frac{3}{4}(x - 6) + 7$$. 2. **Write the inequality clearly:**

1. **State the problem:** Solve the quadratic equation $x^2 + 7x + 2 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Solve the inequality $$\frac{1}{2}(3x - 4) \leq \frac{3}{4}(x - 6) + 7$$. 2. **Write the inequality clearly:**

1. **Stating the problem:** We have a table with two columns: one labeled $m$ and the other labeled $\frac{2m}{2}$. We need to fill in the missing values in the table.

1. **State the problem:** Solve the inequality $$5(x - 5) + 2x - 7 \geq 3(x - 6) + 11x$$. 2. **Expand both sides:**

1. We are given the inequality $$\frac{2}{5} + \frac{3}{7} \geq \frac{x}{35}$$ and need to find the solution set for $x$. 2. First, find a common denominator to add the fractions o

1. **Evaluate g(3) + g(-3)** given $g(x) = 2x + 1$. Use the function definition:

1. **State the problem:** Solve the equation $ (4+6)(4+6x) = 25 - 3.5(x+4) $ for $x$. 2. **Simplify the left side:** Calculate $4+6=10$, so the equation becomes:

1. **State the problem:** Solve the equation $4(11x - 26) = 4 - 4(x + 5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by 4.

1. **State the problem:** Solve the equation $$\frac{18}{t} = 3 + 6$$ for $t$. 2. **Simplify the right side:**

1. **State the problem:** Solve the equation $$\frac{18}{t} = 3 + 6$$ for the variable $t$. 2. **Simplify the right side:**

1. **State the problem:** We need to find the temperature at the mountain top given that the village temperature is 3°C and the mountain top temperature is 12°C lower. 2. **Formula

1. Problem 44 a) Simplify $$3^{-2} : 3^{-4} - \left(\frac{3}{5}\right)^{-2}$$ 2. Use the rule for division of powers with the same base: $$a^m : a^n = a^{m-n}$$

1. **State the problem:** The sea level at low tide is $-2.50$ metres. We want to find the sea level when it is $1.97$ metres above this level. 2. **Formula and explanation:** To f

1. **State the problem:** We are given the function $h(x) = 1 - \sqrt{x}$ and we want to understand its behavior. 2. **Recall the square root function:** The square root function $

1. The problem asks to write an expression for the sequence of operations: add 3 to 5, then divide $z$ by the result. 2. First, add 3 to 5: $$5 + 3$$