🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$12 + \sqrt{x} + 7 = 4$$ where $x$ is a real number. 2. **Combine like terms:** Add the constants on the left side:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x - 3} = 5$$ where $x$ is a real number. 2. **Recall the formula and rules:** The square root function $\sqrt{y}$ is

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x - 3} = 5$$ where $x$ is a real number. 2. **Recall the property of square roots:** For any real number $a \geq 0$,

1. The problem asks to write a function representing the arithmetic sequence 1, 10, 19, 28, ... and graph it. 2. The formula for the nth term of an arithmetic sequence is:

1. The problem asks to graph the function $f(x) = 2\lfloor x \rfloor$ where $\lfloor x \rfloor$ is the floor function, which returns the greatest integer less than or equal to $x$.

1. The problem asks if the function $$K(x) = \frac{5^x}{\sqrt{3} \cdot 6^x}$$ is exponential and to rewrite it in the form $$K(x) = ab^x$$ if it is. 2. Recall that an exponential f

1. **State the problem:** Solve the inequality $$m + 8 \leq 3$$ and graph its solution on the number line. 2. **Formula and rules:** To solve inequalities, we isolate the variable

1. **State the problem:** Jessie has 15 3/4 cups of flour and needs to save 2 cups for a cake. Each batch of bread requires 5 1/2 cups of flour. We want to find how many batches $b

1. **State the problem:** A restaurant pays $3.75 per load plus $12.25 for delivery. The weekly budget is 85. We want to find how many loads $x$ can be cleaned without exceeding th

1. **State the problem:** Evaluate the quadratic expression $$m^2 + 5m + 1$$ when $$m = -4$$. 2. **Recall the formula:** The expression is a quadratic polynomial in $$m$$. To evalu

1. **State the problem:** Solve for $y$ in the linear equation $$8 = y + x$$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equation. This i

1. **State the problem:** Evaluate the expressions $(-4)^2$ and $(-2)^3$. 2. **Recall the rules for exponents:**

1. **State the problem:** Josh wants to buy carpet for his living room floor, which is a rectangle with length 15 feet and width 9 feet. The carpet costs 13 per square foot. We nee

1. **State the problem:** Convert the mixed number $19 \frac{3}{5}$ to a decimal. 2. **Recall the formula:** A mixed number $a \frac{b}{c}$ can be converted to a decimal by calcula

1. **State the problem:** Translate the sentence "43 is the difference of Jenny's height and 21" into an equation using the variable $j$ for Jenny's height. 2. **Understand the sen

1. **State the problem:** Translate the sentence "The product of 7 and Mabel's height is 686" into an equation using the variable $m$ to represent Mabel's height. 2. **Identify key

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and find the value when it equals 10. 2. **Write the expression:** $$\frac{n^2 + n}{n}$$ because $$n

1. The problem states that the line of best fit for attendance based on high temperature is given by the equation $$y = 2.5x - 50$$ where $x$ is the high temperature in °F and $y$

1. **State the problem:** We are given the expression $$n \times n + n$$ and the value $$n = 10$$.

1. The problem is to solve the equation $y = 2x + 3$ for $y$ in terms of $x$. 2. The formula used here is the equation of a straight line in slope-intercept form: $$y = mx + b$$ wh

1. **State the problem:** Jack's shelf can hold either 42 files or 36 stamp albums. He placed 18 files and 18 stamp albums on the shelf. We need to find how many more files can fit