🧮 algebra

1. **State the problem:** We need to find the domain and range of the given graph based on the description. 2. **Domain:** The domain is the set of all possible $x$-values for whic

1. **Stating the problem:** A person pays 14.40 for 60 feet of something. We want to find how much extra she will pay for 40 feet.

1. The problem is to solve the proportion $129.5:9 = x:50$ for $x$. 2. Recall that in a proportion $a:b = c:d$, the cross products are equal, so $a \times d = b \times c$.

1. **State the problem:** A car travels 129.5 km using 9 L of gas. We want to find how far it can go with 50 L of gas at the same rate. 2. **Formula used:** Distance traveled is pr

1. **State the problem:** Solve for $a$ in the equation $$\frac{4}{7}a + 1 = 3$$. 2. **Isolate the term with $a$:** Subtract 1 from both sides:

1. **State the problem:** Solve for $k$ in the equation $$\frac{2}{5}k + 4 = 6$$. 2. **Isolate the term with $k$:** Subtract 4 from both sides:

1. The problem is to simplify the expression for $f$ given by: $$f = 15 \times \frac{15}{10} b + 9.24$$

1. **State the problem:** Solve the equation $X - 5 - 6X = 0$ for $X$. 2. **Combine like terms:** Group the $X$ terms together.

1. **State the problem:** Solve the system of linear equations: $$3x + 2y = 12$$

1. Let's clarify the problem: You want to know how a transformation can be written out mathematically. 2. A transformation in math often means applying a function or operation to a

1. **State the problem:** We have a function that takes an input number, subtracts 8 from it, then divides the result by 2. 2. **Write the formula:** If the input is $x$, the outpu

1. **State the problem:** Solve the equation $x + 7 - 2x = 18$ for $x$. 2. **Combine like terms:** The terms involving $x$ are $x$ and $-2x$.

1. The problem asks to write a compound inequality describing the graph shown. 2. The graph shows a number line with a highlighted segment between 0 and 2, including solid dots at

1. The problem asks to write a compound inequality describing the graph segment between -5 and -4 on the number line. 2. The graph shows a thick magenta line segment from -5 to -4.

1. The problem asks to write a compound inequality describing the graph shown on the number line. 2. The graph shows an open circle at $-5$ and a closed circle at $-4$, with a soli

1. The problem asks to write a compound inequality describing the graph shown on the number line from 675 to 680. 2. The graph has a solid dot at 677, meaning $x \leq 677$ is inclu

1. The problem asks to write a compound inequality describing the graph segment from -289 to -284 with two points at -287 (solid) and -286 (open). 2. A solid point means the value

Problem: Determine the compound inequality represented by a number line with a solid point at $-287$ and an open circle at $-286$. 1. Identify the points.

1. **State the problem:** Zoey wants to make 10 servings of trail mix. The original recipe makes 5 servings and calls for 1 3/4 cups of almonds. We need to find how many cups of al

1. **State the problem:** Evaluate the expression $$3 \cdot 4 - ((-2)^2 - 2)^3$$. 2. **Recall the order of operations:** Parentheses, exponents, multiplication/division, addition/s

1. **State the problem:** Simplify the expression $$\frac{-3 - 5^2}{(-2 + 4)^2}$$. 2. **Recall the order of operations:** Calculate exponents first, then addition/subtraction, and