🧮 algebra

1. **State the problem:** Solve the equation $$\frac{3x - 4}{4} = 5x - 1$$. 2. **Multiply both sides by 4** to eliminate the denominator:

1. The problem asks to find the value of $k$ where $k = \frac{f(6) - f(1)}{6 - 1}$ for the function $f(x) = 5x - 2$. 2. First, calculate $f(6)$ and $f(1)$:

1. **State the problem:** You receive 15% of the profit from a car wash. The total profit is 300. We need to find how much money you receive. 2. **Formula:** To find the amount you

1. **State the problem:** We need to find what percent of 12 is 3. 2. **Formula:** The percentage is found by the formula $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole

1. The problem asks: 12 is what percent of 50? 2. To find what percent one number is of another, use the formula:

1. **State the problem:** We need to find the number $x$ such that 12% of $x$ equals 48. 2. **Write the equation:** 12% means 12 per 100, so we write:

1. **State the problem:** We need to find what percent of 125 is 50. 2. **Formula:** The percent $P$ of a number $A$ that equals another number $B$ is given by:

1. The problem asks: "8 is what percent of 5?" This means we want to find the percentage $p$ such that $8$ is $p\%$ of $5$. 2. The formula to find the percentage is:

1. Problem: What number is 35% of 80? 2. Formula: To find a percentage of a number, use the formula $$\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}$$

1. **State the problem:** Simplify the expression $\frac{2x^2}{2x}$. 2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{

1. **State the problem:** Simplify the expression $2x^2 \cdot 2x$. 2. **Recall the rule for multiplying coefficients and variables:** When multiplying terms with the same base, add

1. **State the problem:** Add the fractions $\frac{2}{3}$ and $\frac{1}{4}$. 2. **Formula:** To add fractions, use the formula $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$.

1. **State the problem:** Multiply the fractions $\frac{1}{2}$ and $8 \frac{1}{8}$.\n\n2. **Convert the mixed number to an improper fraction:**\n$8 \frac{1}{8} = \frac{8 \times 8 +

1. **State the problem:** Calculate the value of the expression $$n = (1 \times 3) + \left[1 \times 3 \times \frac{1}{4}\right] + \left(3 \times 3 \times \frac{1}{2}\right) + \left

1. **State the problem:** Solve the linear equation $$3(v + 4) = -3(4v - 8) + 5v$$ for the variable $v$. 2. **Apply the distributive property:** Multiply each term inside the paren

1. **Stating the problem:** We want to simplify the expression $$\frac{x^2 - 2x}{x - 2}$$ and check if it equals $$x$$. 2. **Formula and rules:** To simplify a rational expression,

1. **State the problem:** Solve the linear equation $$-4(-6u+6) - 5u = 7(u-1) - 2$$ for the variable $u$. 2. **Apply the distributive property:** Multiply inside the parentheses.

1. The problem is to understand and analyze the linear function $y=0.5x+3.5$. 2. This is a linear equation in slope-intercept form $y=mx+b$, where $m$ is the slope and $b$ is the y

1. **State the problem:** We are given amounts of vinegar, water, and total cleaning solution in cups, and we want to understand the relationship between these quantities.

1. **Stating the problem:** Rearrange the equation $$\sqrt{\frac{m}{p}} = c$$ to make (a) $$m$$ the subject and (b) $$p$$ the subject. 2. **Recall the formula and rules:** The squa

1. We are given the function $f(x) = 2x + 2$ and asked to find the value of $x$ when $f(x) = 4$. 2. The problem is to solve the equation: