🧮 algebra

1. The problem is to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. We start by multiplying both sides of the equation by the denominator $x-3$ to eliminate the fraction:

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Solve the quadratic equation $$x^2 + 6x - 2 = 0$$. 2. **Formula used:** The quadratic formula to solve $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Simplify the expression $0.5(b+7)-0.3b+4$. 2. **Apply the distributive property:** Multiply $0.5$ by each term inside the parentheses.

1. **State the problem:** Simplify the expression $(x-9)-(4-2x)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the second group:

1. **State the problem:** Simplify the expression \(\frac{7x + 19}{2x - 7} + 5x + 12\). 2. **Rewrite the problem:** We want to add the rational expression \(\frac{7x + 19}{2x - 7}\

1. The problem asks to write the fraction $-\frac{3}{7}$ as a decimal, using bar notation if necessary. 2. To convert a fraction to a decimal, divide the numerator by the denominat

1. The problem asks: "Golden Gate Park is about ___ % larger than Central Park." We need to find the percentage increase from Central Park's area to Golden Gate Park's area. 2. The

1. **State the problem:** Simplify the expression $\left(\frac{1}{2}x - 3\right) + \left(\frac{1}{6}x + 1\right)$. 2. **Write the expression:**

1. The problem asks to convert the improper fraction $\frac{15}{2}$ into a mixed number. 2. A mixed number consists of a whole number and a proper fraction.

1. The problem involves multiplying the fractions $\frac{19}{6}$ and $\frac{2}{15}$, finding the GCF, and converting $\frac{5}{2}$ to a mixed number. 2. To multiply fractions, mult

1. The first problem is to write $3 \frac{1}{6}$ as an improper fraction. 2. To convert a mixed number to an improper fraction, use the formula:

1. **State the problem:** Simplify the expression $3 \frac{1}{6} \div \frac{15}{2}$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** Subtract the expressions $$\frac{-5}{2u} - \frac{7}{6u^2}$$ and simplify the result.

1. **State the problem:** We want to analyze the rational function $$y = \frac{2x^2 - 4}{2x^4 - 5x^2 + 2}$$ to find points of exclusion (POEs), vertical asymptotes (VAs), zeros (x-

1. **State the problem:** Solve the equation $$(z+1)(z+3)=0$$ for $z$. 2. **Formula and rule:** The zero product property states that if the product of two factors is zero, then at

1. **State the problem:** We are given a cost of 176 for 11 hours and want to find the cost for 374 hours using proportions. 2. **Formula used:** The unit rate is calculated as cos

1. **State the problem:** Solve the system of equations: $$A + B = 2$$

1. **State the problem:** Solve the equation $30 = (2x + 9) + 5$. 2. **Simplify the right side:** Combine like terms inside the parentheses and constants.

1. **Énoncé du problème** : On considère la fonction définie sur l'intervalle $I = ]-1;0[$ par $$g(x) = \frac{1}{x(1+x)^2}.$$