🧮 algebra

1. **State the problem:** Solve the inequality $120 + 25x + 10x \geq 300$. 2. **Combine like terms:** $25x + 10x = 35x$, so the inequality becomes:

1. **State the problem:** Solve the system of equations by graphing: $$h = d^2 - 16d + 60$$

1. **Problem statement:** Given the function $f(x) = x^2 + 1$, find the values of $f(0)$, $f(5)$, $f(-5)$, $f(-x)$, $-f(x)$, $f(x+3)$, $f(4x)$, and $f(x+h)$. 2. **Formula:** The fu

1. **State the problem:** Solve the equation $9.4 + 64x^2 = 53$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $$4x^2 + 7 = 71$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 7 from both sides:

1. Stating the problem: If 12% of a number is 48, find the number. 2. Formula used: Percentage problem formula is $$\frac{\text{percentage}}{100} \times \text{number} = \text{value

1. **State the problem:** Solve the inequality $x + 3y \ge 9$ for $y$ in terms of $x$. 2. **Isolate $y$:** To express $y$ in terms of $x$, subtract $x$ from both sides:

1. **State the problem:** Roy and 2 friends (3 people total) each buy a hot dog for $3, fries for $2.49, and a drink for $2.50. They have a coupon for $1 off each drink. We need to

1. **State the problem:** We need to find which expressions correctly represent the total amount of money Alice spends after attending 8 art classes, where each class she buys a bo

1. **Problem Statement:** We have a graph with a solid line passing through the origin with slope 1, and the region above and to the left of this line is shaded.

1. The problem is to solve the equation $x + y = -4$ for one variable in terms of the other. 2. The equation $x + y = -4$ is a linear equation with two variables. To solve for one

1. The problem is to evaluate the expression: $$6 [51 - (7 - 3)^2]$$. 2. According to the order of operations (PEMDAS/BODMAS), we first solve expressions inside parentheses, then e

1. **State the problem:** We need to graph two lines given by the equations: Line A: $2x - y = 5$

1. The problem is to not expand and simplify the given expression. 2. Since the instruction is to leave the expression as is, we do not perform any algebraic expansion or simplific

1. The problem is to find the value of a number or expression that equals 81. 2. Since the user states the answer is 81, let's consider a common algebraic problem: solving for $x$

1. **State the problem:** Given a slope (pitch) of $\frac{5}{12}$ and a run (horizontal distance) of 10, find the rise (vertical height). 2. **Recall the formula for slope:**

1. **State the problem:** We need to find a pricing structure for Faster Fitness so that the total cost for 14 classes is the same as Drop In Fitness. 2. **Given:** Drop In Fitness

1. The problem involves understanding the relationship between hours worked and weekly earnings. 2. We can use the formula for hourly wage: $$\text{Hourly Wage} = \frac{\text{Weekl

1. **State the problem:** We need to express the graph as a piecewise function $f(x)$ based on the two line segments described. 2. **Identify the points and slopes:**

1. **State the problem:** We need to express the graph as a piecewise function based on the two line segments given. 2. **Identify the points and intervals:**

1. **Stating the problem:** We want to understand the properties of addition illustrated by the expressions: $b + c = d$