🧮 algebra

1. **State the problem:** Solve the equation $$2c + 5 - c = 14$$ for the variable $c$. 2. **Combine like terms:** On the left side, combine $2c$ and $-c$:

1. The problem is to understand and graph the function $f(x) = \sqrt{x + 2}$. 2. This function is a square root function shifted horizontally. The general form is $f(x) = \sqrt{x -

1. **State the problem:** Simplify the expression $$2(4x - 4) - 3(x - 3)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Evaluate the expression $$\frac{xy}{z} + \frac{5}{12}$$ for $$x = -4$$, $$y = -3$$, and $$z = 6$$. 2. **Write the formula and substitute values:**

1. The problem asks to identify the property used to multiply the expression $-3(2x + 1)$. 2. The expression involves multiplying a single term outside the parentheses by each term

1. **State the problem:** Solve the equation $x - 5.7 = 19$ for $x$. 2. **Formula and rules:** To isolate $x$, add $5.7$ to both sides of the equation. This uses the addition prope

1. The problem states: "Six subtracted from a number gives 44." We need to write this as an equation using $x$ to represent "a number." 2. "Six subtracted from a number" means we t

1. The problem asks to write the sentence "The product of 3 and the sum of -69 and a number gives -24" as an equation using $x$ to represent the number. 2. The phrase "product of 3

1. **State the problem:** Solve the equation $$4x - 4 = 5(x - 9)$$. 2. **Apply the distributive property:** Expand the right side:

1. The problem asks to fill in the blank in the sentence: "By the ________ property of equality, we may multiply or divide both sides of an equation by any nonzero number without c

1. The problem asks to write the sentence "The quotient of -112 and 8 amounts to -14" as an equation. 2. The word "quotient" means division, so the quotient of -112 and 8 is writte

1. **State the problem:** Solve the equation $$- \frac{5}{4} x = \frac{10}{20}$$ for $x$. 2. **Simplify the right side:** $$\frac{10}{20} = \frac{1}{2}$$.

1. El problema nos da varias ecuaciones y nos pide para la primera: identificar la cónica, obtener sus elementos y graficarla. 2. La primera ecuación es $$y^2 = -20x$$.

1. The problem asks for the root of 14, which typically means finding the square root of 14. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. The problem asks for the root of 36. 2. The root usually refers to the square root, which is the number that when multiplied by itself gives the original number.

1. El problema nos da varias ecuaciones y nos pide para la primera: (1) identificar la cónica, (2) obtener sus elementos, y (3) graficarla. 2. La ecuación dada es $$y^2 = -20x$$.

1. 問題の説明：練習5の式を代入し、展開して整理します。 2. まず、練習5の式を確認します（ここでは仮に練習5の式を $a(x+y)$ とします）。

1. The problem is to find the remainder when 30 is divided by 100, which is expressed as $30 \% 100$. 2. The modulo operation $a \% b$ gives the remainder when $a$ is divided by $b

1. **State the problem:** We are given the values $A=129$, $a=4$, and $t=18$ and need to find $T$ in the formula for the sum of an arithmetic series. 2. **Recall the formula:** The

1. **Stating the problem:** Solve the equation $$x^x = 9\sqrt{\frac{1}{3}}$$ for $x$. 2. **Rewrite the right side:** Note that $$9\sqrt{\frac{1}{3}} = 9 \times \left(\frac{1}{3}\ri

1. El problema nos da varias ecuaciones y nos pide para la primera: (1) identificar la cónica, (2) obtener sus elementos, y (3) graficarla. 2. La ecuación dada es $$y^2 = -20x$$.