🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$\frac{x + 4}{5} + \frac{2x - 1}{3} = 1.$$\n\n2. **Formula and rules:** To solve equations with fractions, find a common de

1. **State the problem:** Simplify the expression $$2 \times \frac{4}{5} + \frac{14 + 3x}{4}$$. 2. **Apply multiplication:** Multiply 2 by the fraction \(\frac{4}{5}\):

1. **State the problem:** Simplify the expression $$6 \div 2(15 + 20)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. Let's start by stating the problem clearly: You want to understand the simplification step at part 7. 2. Simplification in algebra often involves reducing expressions by canceli

1. **State the problem:** Convert a mixed number to an improper fraction. 2. **Formula:** For a mixed number $a \frac{b}{c}$, the improper fraction is given by:

1. The problem is to solve the equation by isolating $y$ first. 2. Suppose the equation is given in the form $Ax + By = C$.

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$.\n2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations.\n3. Subtract 3 from

1. Solve the system: $$\begin{cases} x + y + z = 6 \\ 2x - y + 3z = 14 \\ -x + 4y - z = 2 \end{cases}$$ 2. Solve the system: $$\begin{cases} 3x + 2y - z = 7 \\ x - y + 4z = 10 \\ 2

1. **Problem Statement:** Solve the system of 10 simultaneous equations with 3 variables $x$, $y$, and $z$ where all solutions are whole numbers. 2. **General Approach:** For simul

1. The problem is to solve the system of equations by eliminating $y$. 2. Suppose the system is:

1. State the problem: Solve the system of simultaneous equations with three variables $x$, $y$, and $z$ where all solutions are whole numbers. 2. Example system:

1. **State the problem:** Solve the equation $$\frac{2x-5}{3} - \frac{x}{2} = \frac{4-x}{6}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, fin

1. **Planteamiento del problema:** Factorizar el trinomio $$x^2 + 2x - 3$$. 2. **Fórmula y reglas importantes:** Para factorizar un trinomio de la forma $$ax^2 + bx + c$$ cuando $$

1. El problema es factorizar el trinomio $49x^2 + 2x - 3$. 2. Para factorizar un trinomio de la forma $ax^2 + bx + c$, buscamos dos números que multiplicados den $a \times c$ y sum

1. El problema es factorizar la expresión $y(y-6) + 9(y-6)$ usando factor común. 2. La fórmula para factor común es $a b + a c = a(b + c)$, donde $a$ es el factor común.

1. **State the problem:** Solve the equation $4R - 3 = 3(3R + 4)$ for $R$. 2. **Write the formula and rules:** We will use the distributive property to expand the right side and th

1. **State the problem:** Simplify the expression in the top-left rectangle: $17^2 - 286$. 2. **Recall the formula and rules:** Calculate the square of 17 and then subtract 286.

1. **State the problem:** Solve the absolute value equation $$15 = 5|3x + 3|$$ for $x$. 2. **Isolate the absolute value expression:** Divide both sides by 5:

1. **State the problem:** Solve the absolute value equation $$\frac{2|x - 3|}{5} = 6$$ for $x$. 2. **Formula and rules:** To solve equations involving absolute values, recall that

1. **State the problem:** Solve the compound inequality $$5 < \frac{4x - 16}{8} < 8$$ and find the range for $$x$$. 2. **Recall the rule for compound inequalities:** We can multipl

1. **Stel het probleem vast:** We willen weten hoeveel euro 1 kilogram sojabonen kost, gegeven dat 320 gram sojabonen €1,45 kost. 2. **Formule:** De prijs per kilogram (1000 gram)