🧮 algebra

1. **Simplify the expression** $9 - 2x - 7 + 4x$. 2. **Use the Commutative Property** to reorder terms so like terms are together:

1. **State the problem:** Solve the quadratic equation $2x^2 + 6x = 2$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to simplify the expression $C - \frac{2}{3} \leq \sin(x)$.\n\n2. This is an inequality involving the sine function and a constant $C$. We want to understand the r

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:** Simplify the expression $4x - (2x + 3)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign:

1. **State the problem:** We have a factory with male and female workers. The number of female workers is $\frac{4}{7}$ of the number of male workers.

1. Stating the problem: Simplify the expression $\frac{2}{3} - \frac{3}{7}$.\n\n2. To subtract fractions, they must have a common denominator. The denominators here are 3 and 7.\n\

1. The problem is incomplete as the denominator of the fraction $\frac{3}{ }$ is missing. 2. To evaluate or simplify a fraction, both numerator and denominator must be specified.

1. Das Problem lautet: Löse jede der Aufgaben. Da keine spezifische Aufgabe angegeben ist, kann ich nur allgemeine Hinweise geben. 2. Um eine algebraische Gleichung zu lösen, verwe

1. **Problem:** Entscheide, ob die Aussage "Die erste Winkelhalbierende hat die Funktionsgleichung $f(x) = x$" richtig oder falsch ist. 2. **Formel und Erklärung:** Die erste Winke

1. **Problem statement:** Evaluate the following expressions without using a calculator. 2. **Part (a):** Evaluate $-2 - \frac{3}{5}$ and $-2 + \frac{3}{5}$.

1. The problem asks to determine the constant of proportionality $k$ for the first table and fill in the missing values. 2. Recall that in a proportional relationship, $y = kx$, wh

1. **State the problem:** Solve the system of linear equations labeled (l): $$3x - y = 4$$

1. **Problem 4:** Given the table showing time in minutes and pool water in gallons, the relationship is proportional. We need to confirm and fill in missing values if any. 2. The

1. Das Problem ist, einen Ausdruck oder eine Gleichung zu vereinfachen. 2. Vereinfachen bedeutet, den Ausdruck so umzuformen, dass er kürzer oder leichter zu verstehen ist, ohne de

1. **State the problem:** Find the points of intersection between the functions $$f(x) = x^2 + 4x$$ and $$g(x) = \sqrt{x^2 + 4x}$$. 2. **Set the functions equal to find intersectio

1. Das Problem lautet: Berechne den Scheitelpunkt der quadratischen Funktion $$f(x) = 4x^2 + 8x - 12$$ und gib die Scheitelpunktform an. 2. Die Scheitelpunktform einer Parabel laut

1. **State the problem:** We are given that after a 20% price decrease, the GST on a computer is 150. We need to find the GST on the computer before the price decrease. 2. **Define

1. **Stating the problem:** We have a price that undergoes a series of percentage changes: an increase of 20%, a decrease of 10%, an increase twice of 5%, and a one-time increase o

1. **Stating the problem:** We have a sequence of patterns made of unit squares forming rectangles. The first four patterns have dimensions and perimeters as follows: - Pattern 1:

1. **Problem statement:** Find the range of the functions: