🧮 algebra

1. The problem asks to find the fraction represented by point B on a number line. 2. The number line has points at 3/4, B, -1/2, 1/4, C, and 0, with B located between 3/4 and -1/2.

1. **State the problem:** Solve the linear equation $3x - 8 = 10$ for $x$. 2. **Use the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add 8 t

1. The problem is to find the sum of the numbers $(-26,9)$ and $(-33)$. 2. First, clarify the notation: $(-26,9)$ appears to be a coordinate or a pair, but since the second number

1. **Problem statement:** We are given that $f(g(x)) = x$ and the graph of $y = g(x)$ is increasing and concave up, resembling a logarithmic function from approximately $(-4,0)$ to

1. **State the problem:** Simplify or expand the expression $x^3(y - 5)(x - 8)$. 2. **Recall the distributive property:** To expand, multiply each term in one parenthesis by each t

1. **Problem:** Solve the equation $2000x - 0.03 = 6900$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations: addition/subtraction and

1. **State the problem:** Solve the equation $$2(x - 9) = 10$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. This helps us expand expressions like $$2(x - 9)$$.

1. **State the problem:** A tree surgeon finds that 3 out of every 10 ash trees inspected have ash die-back disease and must be felled. She fells 45 ash trees. We need to find how

1. **State the problem:** Find the equation of the line of symmetry of the curve for the quadratic function $$y = 2x^2 - 4x + 3$$.

1. **State the problem:** Simplify the expression $$2(7+2\times 3)+4 \div \frac{1}{6}$$. 2. **Recall order of operations (PEMDAS/BODMAS):**

1. **Problem Statement:** Solve the proportion $\frac{3}{5} = \frac{13}{x}$ to find the missing side length $x$. 2. **Formula Used:** For proportions, if $\frac{a}{b} = \frac{c}{d}

1. **State the problem:** We have a ratio table with two rows, Fruit and Vegetables, and three columns. The values are: Fruit: 2, 3, 6

1. **State the problem:** Solve the system of linear equations: $$y = x + 8$$

1. **State the problem:** We need to find the total number of students based on the line plot showing the number of students scoring each quiz score from 5 to 10. 2. **Understand t

1. **State the problem:** Solve the system of equations: $$\begin{cases} x = 3y \\ 2x + 4y = 10 \end{cases}$$

1. **State the problem:** Factor the quadratic expression $x^2 + 14x + 24$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. **State the problem:** Factor the quadratic expression $$y^2 - 9y + 18$$. 2. **Recall the factoring formula:** For a quadratic of the form $$y^2 + by + c$$ where the leading coe

1. **State the problem:** Solve the equation $-\frac{7}{2} = -\frac{2}{4}$. 2. **Simplify the right side:**

1. **State the problem:** Given the table of values for $x$ and $y$, find the linear equation that relates $y$ to $x$. 2. **Identify the pattern:** From the table, as $x$ increases

1. **State the problem:** We need to find the linear equation $y = mx + b$ that fits the given table of values: $$\begin{array}{c|c} x & y \\ \hline 2 & 0 \\ 3 & 1 \\ 4 & 2 \\ 5 &

1. **State the problem:** Katrina takes 7 hours to fill the pie alone. Together, Katrina and Mei take 3 hours. We need to find how long Mei takes alone. 2. **Use the work rate form