🧮 algebra

1. **State the problem:** Solve the equation $$7(x+6)+18 = 9(x+1)-3$$ for $x$. 2. **Write down the equation:** $$7(x+6)+18 = 9(x+1)-3$$

1. **Problem:** Find the 10th term of the arithmetic sequence where the first term $a_1=3$ and the common difference $d=5$. 2. **Formula:** The $n$th term of an arithmetic sequence

1. **Problem:** Emma spent $75$ buying a bicycle and $27$ repairing it. She sold it for $40\%$ more than the total spent. Compare the selling price (Quantity A) to $140$ (Quantity

1. **State the problem:** Solve the linear equation $67x - 36y = 18$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. T

1. Let's start by understanding the problem: You want to know how to determine the value $\frac{3}{8}$ from a graph. 2. When looking at a graph, especially one representing fractio

1. **State the problem:** John and Tom collected money for charity on Monday, Tuesday, and Wednesday. We know the total collected on Monday ($30) and Tuesday ($40). We want to find

1. **State the problem:** We need to calculate the value of $$73837373828 \div 0$$. 2. **Recall the rule:** Division by zero is undefined in mathematics. This means you cannot divi

1. **State the problem:** We need to write an inequality for an absolute value function graphed as an inverted V with vertex at approximately $$(3, 1)$$, passing through points $$(

1. **State the problem:** We need to check if $-7$ is a solution to the equation $$-9f = 70 - f$$ by substituting $f = -7$ and comparing both sides. 2. **Substitute $f = -7$ into t

1. **State the problem:** We need to check if $-3$ is a solution to the equation $$x + 16 = 19$$ by substituting $x$ with $-3$ and verifying if both sides are equal. 2. **Substitut

1. **State the problem:** Solve the quadratic equation $$19x^2 + 380x + 1899 = 0$$ by completing the square. 2. **Divide the entire equation by the coefficient of $$x^2$$ to make i

1. **State the problem:** Solve the quadratic equation $$1.8x^2 - 5.9x - 3.4 = 1.4$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We want to find the unit rate of kilometers to miles given that $\frac{8}{10}$ kilometers correspond to $\frac{5}{10}$ miles. 2. **Write the ratio:** The

1. **State the problem:** We are given expressions involving length and width, and asked to use the distributive property to write expressions for the perimeter. Also, for a regula

1. **State the problem:** Kari wants to check if the expressions $x^2 + x$ and $x(2x + 1)$ are equivalent by substituting $x = 0$. 2. **Evaluate both expressions at $x = 0$:**

1. **State the problem:** We start with the equation $$\frac{1}{2}x - 4 = 8$$ and multiply both sides by $$-1$$. We want to determine which statements about the resulting equation

1. **State the problem:** We are given the first four terms of a quadratic sequence: $3$, $10$, $19$, $30$. We need to find a formula for the $n$th term, $T_n$, in terms of $n$. 2.

1. **State the problem:** We are given the first 6 terms of a quadratic sequence: $-3, 3, 13, 27, 45, 67$. We need to find a formula for the $n$th term, $T_n$. 2. **Recall the form

1. **State the problem:** We need to evaluate the expression $$2.5 \times 10^{3}$$. 2. **Recall the rule:** Multiplying by $$10^{3}$$ means multiplying by 1000 because $$10^{3} = 1

1. The problem is to complete the graph based on the given table of values. 2. The table shows three columns: the first column is the input $x$, the second column is $x+2$, and the

1. **State the problem:** We have the temperature model $$T = -5t + 200$$ where $T$ is temperature in °F and $t$ is time in minutes. 2. **Identify intercepts:**