🧮 algebra

1. **State the problem:** Solve the expression $\frac{1}{2} \times (6k+1) \times 3k$. 2. **Write the expression clearly:**

1. **Problem statement:** Solve the system of equations: $$\begin{cases} s + c = m \\ s - c = 2 \end{cases}$$

1. **State the problem:** We are given values $e = 1$ and $f = 12$, and we need to find the value of the expression $$11e + 7f$$. 2. **Write the expression with given values:** Sub

1. **State the problem:** Evaluate the expression $$\frac{12d - e}{2}$$ given that $$d = 11$$ and $$e = 8$$. 2. **Write the formula and substitute values:** Replace $$d$$ and $$e$$

1. **State the problem:** Simplify the expression $1 \frac{3}{5} - 2 \frac{1}{3} + \frac{2}{5} \div 3$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Find the equation of a line passing through the point $(-4,2)$ and perpendicular to the line given by $3x + 4y - 7 = 0$. 2. **Identify the slope of the gi

1. **State the problem:** Find the equation of a line passing through the point $(-4,2)$ and perpendicular to the line given by $3x + 4y = 0$. 2. **Rewrite the given line in slope-

1. The problem is to interpret the time given as "10h 40mn 45s" and understand the number 8 in the context. 2. The time is given in hours, minutes, and seconds: 10 hours, 40 minute

1. **State the problem:** We are given a table with values of $x$ and $y$: $$\begin{array}{c|cccc}

1. **State the problem:** We are given a table showing the baby's age $x$ in months and the corresponding average length $y$ in inches: | Age $x$ (months) | 0 | 1 | 2 | 3 |

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. **Stating the problem:** We need to find the shape of the solution region for the system of inequalities:

1. **State the problem:** Solve the equation $$35=\frac{1}{2}\cdot (x+30)$$ for $x$. 2. **Use the formula and rules:** To solve for $x$, we need to isolate $x$ on one side. Since $

1. **Stating the problem:** We need to determine the shape of the solution region for the system of inequalities:

1. Stating the problem: Simplify the expression $$\frac{4ab^3}{6a^2b}$$. 2. Write the expression as a fraction: $$\frac{4ab^3}{6a^2b}$$.

1. **Stating the problem:** Find the value of $x$ from the equation:

1. **Stating the problem:** Simplify the expression \(\log_{7} 77x - 20\log_{7} x - 5\log_{7} (x+1)\). 2. **Recall logarithm properties:**

1. **State the problem:** Simplify the expression $$\left(\frac{3}{2} + \left(\frac{4}{5} - \left(\frac{5}{3} \div \frac{7}{6}\right)\right)\right) \times \left(\frac{9}{4} \div \f

1. **State the problem:** We need to find the remainder when the number $$N = \frac{1^4 + 2024^4 + 2025^4}{1^3 + 2024^3 + 2025^3}$$ is divided by 2026. 2. **Rewrite the problem:**

1. **Problem statement:** We have a sequence of six distinct positive integers in strictly increasing order, where each term (except the first) is a multiple of the previous term.

1. **State the problem:** We want to find the value of $\frac{1}{2} - \frac{1}{10}$. 2. **Find a common denominator:** The denominators are 2 and 10. The least common denominator (