🧮 algebra

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

1. The problem asks to use inductive reasoning to predict the next number in the sequence: 5, 10, 15, 20, 25. 2. Inductive reasoning involves observing the pattern in the given num

1. **State the problem:** Solve the equation $$4(3x - 8) + 5 = x - 5$$ for $x$ and give a reason for each step. 2. **Distribute the 4:** Apply the distributive property $$a(b + c)

1. The problem asks to identify which of the six given graphs represent functions. 2. A function is defined as a relation where each input (x-value) has exactly one output (y-value

1. Let's consider a random algebra problem: Solve for $x$ in the equation $$2x + 5 = 15$$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract

1. **State the problem:** We need to interpret the slope and y-intercept of a linear function that models Kelly's savings as she walks dogs. 2. **Identify the variables:** The hori

1. **State the problem:** We need to find the length of the alligator at birth and its growth rate based on the linear relationship shown in the graph. 2. **Identify given data:**