🧮 algebra

1. **Stating the problem:** (a) Find the number $x$ such that 75% of $x$ is 36.

1. **State the problem:** Ahmad's chocolate bar is 74% cocoa, and the total weight is 69 grams. We need to find how many grams of cocoa it contains, rounded to the nearest tenth. 2

1. The problem is to simplify the expression $Ex$. 2. Since $E$ is a constant and $x$ is a variable, the expression $Ex$ is already in its simplest form.

1. The problem states: Forty-five less a number is equal to the product of 3 and the sum of the number and 7. 2. Let the number be $x$.

1. **Énoncé du problème :** Simplifier l'expression rationnelle $$\frac{7}{5a^{2}b} + \frac{3}{2a^{3}} - \frac{1}{b^{2}}$$ et indiquer les restrictions.

1. **State the problem:** Rearrange the equation $$a = b \left( \frac{1}{c} - \frac{1}{d} \right)$$ to isolate $c$. 2. **Start by dividing both sides by $b$ to isolate the parenthe

1. The problem states: "The product of 5 and the sum of -6 and a number is -20." We need to write this as an equation using $x$ to represent "a number."\n\n2. The phrase "the sum o

1. The problem states: "A number added to -6 is -7." We need to write this as an equation using $x$ to represent "a number."\n\n2. The phrase "a number added to -6" means $x + (-6)

1. **State the problem:** Rearrange the equation $$\left(a + \frac{b}{c}\right)(d - e) = f$$ to isolate the variable $a$. 2. **Formula and rules:** To isolate $a$, we need to undo

1. The problem is to simplify and solve the expression $\left(a + \frac{b}{c}\right)(d - e) = f$ for $a$. 2. Start by expanding the left side using the distributive property: $$\le

1. **State the problem:** We need to find the fraction of juice purchased that is orange juice given that out of every 192 containers, 82 are orange juice. 2. **Formula:** The frac

1. **Problem Statement:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and Rules:** To solve rational equations, multiply both sides by the denominator to elim

1. **State the problem:** We are given that 25 states have four-star hotels out of a total of 50 states. We need to find: (a) The fraction of states with at least one four-star hot

1. **State the problem:** We need to find what fraction of a 12-hour work shift is represented by 6 hours. 2. **Formula:** The fraction of the work shift is given by \( \frac{\text

1. **State the problem:** Find the cube root of 81, which is written as $\sqrt[3]{81}$. 2. **Recall the definition:** The cube root of a number $a$ is a number $b$ such that $b^3 =

1. The problem is to find the value of $\sqrt{81}$.\n\n2. The square root of a number $x$ is a value that, when multiplied by itself, gives $x$.\n\n3. We use the formula $\sqrt{a}

1. **State the problem:** Solve the inequality $-4x < 12$ for $x$. 2. **Recall the rule:** When dividing or multiplying both sides of an inequality by a negative number, the inequa

1. **State the problem:** Solve the compound inequality $$\frac{1}{6} < \frac{2x - 13}{12} \leq \frac{2}{3}$$. 2. **Understand the inequality:** We want to find all values of $x$ s

1. The problem is to provide a grade 7 level answer, so I will explain a simple algebra problem step-by-step. 2. Let's solve the equation $2x + 3 = 11$.

1. **State the problem:** We have a two-step function machine where the input $x$ is first divided by 5, then 4 is subtracted from the result to produce the output $y$. Given some

1. Planteamos el problema: Resolver la expresión $$[413+2] - 9(5)-4) \div 5 \cdot$$ 2. Primero, interpretamos la expresión correctamente. Parece que hay un error de paréntesis, per