🧮 algebra

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **Problem:** Simplify the expression $8x^2 y^3 \cdot 2x^3 y$. 2. **Formula and rules:** When multiplying terms with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$.

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e

1. The problem is to evaluate the expression S = -2(-1 + 6). 2. First, simplify inside the parentheses:

1. Problemet är att hitta skärningspunkten P mellan linjerna $L_1: y = 2x - 4$ och $L_2: y = x - 1$. 2. Skärningspunkten är där båda linjernas $y$-värden är lika, alltså där $2x -

1. **State the problem:** Solve the quadratic equation $$84 = 7u^2 + 28$$ for the real number $u$, rounding to the nearest hundredth. 2. **Rewrite the equation:** Subtract 84 from

1. **State the problem:** Sarah is 5 years older than her brother, and the sum of their ages is 35 years. 2. **Identify the variable:** Let $x$ represent her brother's age.

1. **State the problem:** Sarah is 5 years older than her brother, and the sum of their ages is 35 years. 2. **Define variables:** Let $x$ represent her brother's age.

1. **State the problem:** Sarah is 5 years older than her brother, and the sum of their ages is 35 years. 2. **Define variables:** Let $x$ represent the brother's age.

1. The problem asks: How much money does he have left if he bought 5 cards? 2. To solve this, we need to know the initial amount of money he had and the cost of each card.

1. **State the problem:** We want to find the equation that represents the amount of money $y$ he has left after some transactions involving $x$. 2. **Analyze the options:** The op

1. **State the problem:** Kiko saved 120 and buys gift cards costing 10 each. We want to find the unknown value represented by a variable.

1. **State the problem:** We need to find the value of the expression $5b + c^3$ when $b=7$ and $c=4$. 2. **Write the expression:** The expression is $5b + c^3$.

1. **State the problem:** Find the x-intercepts of the function and solve the equation $3x^2 - 72 = 0$ using the square root property. 2. **Identify x-intercepts:** Given points $(

1. **Problem statement:** Prove that for all natural numbers $a$ and $b$, the equation $$(a^2 + b^2)^2 - (a^2 - b^2)^2 = (2ab)^2$$ holds true. 2. **Formula and rules:** This proble

1. **State the problem:** Simplify the expression $$\frac{2y - 8}{y^2 - 3y - 4} + \frac{3}{y + 1}$$. 2. **Factor the denominators and numerator where possible:**

1. The problem asks for the coefficient of the variable in the expression $5z + \left(9 \div 3\right)$. 2. The expression consists of two parts: a variable term $5z$ and a constant

1. **State the problem:** Solve the equation $$\sqrt{x} - 1 = x - 3$$ and determine which statements about the solutions are true. 2. **Isolate the square root:** Add 1 to both sid

1. **State the problem:** Simplify the expression $$\left(\sqrt[8]{16x^{12}}\right)^6$$. 2. **Recall the rules:** The eighth root can be written as a fractional exponent: $$\sqrt[8

1. **State the problem:** Simplify the expression $$\left(\sqrt[8]{16x^{12}}\right)^6$$. 2. **Recall the rule for radicals and exponents:**

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at coordinates $(1,1)$ a