🧮 algebra

1. **State the problem:** Solve for $d$ in the equation $$6d - \frac{11}{2} = 2d - \frac{13}{2}$$. 2. **Isolate the variable terms on one side:** Subtract $2d$ from both sides to g

1. The problem is to analyze the linear function $y = x + 4$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. The problem asks to express a set in both interval notation and set builder notation. 2. Interval notation describes all numbers between two endpoints, using brackets [ ] for in

1. **State the problem:** We are given the quadratic function $y = -2(x+4)^2 - 1$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function in vertex form $y =

1. **State the problem:** Evaluate $\{x \mid x=4\}$. 2. **Use the definition of set-builder notation:** This means “the set of all $x$ such that $x=4$.”

1. **State the problem:** We need to find the average score of Alice, Chris, Dan, and Emeril from their golf scores. 2. **List the scores:**

1. The problem is to simplify the expression $-i^2$. 2. Recall that $i$ is the imaginary unit defined by the property $i^2 = -1$.

1. The problem asks to find the reciprocal of the number $\frac{1}{14}$. 2. The reciprocal of a number $x$ is defined as $\frac{1}{x}$. This means you flip the numerator and denomi

1. **State the problem:** We need to find a number such that the difference between the number and 9 equals 37 less the number. 2. **Set up the equation:** Let the number be $x$. T

1. **State the problem:** We need to perform the subtraction \( \frac{1}{7} - \frac{1}{11} \) and simplify the answer. 2. **Formula and rules:** To subtract fractions, we find a co

1. **State the problem:** Amy charges 65 per student for a 6-week session and collects a total of 1690 from one group. We need to find the number of students in that group. 2. **Fo

1. **State the problem:** Simplify the expression $$-7 + (19)(9) + 2$$. 2. **Recall the order of operations:** Multiplication comes before addition and subtraction.

1. The problem asks to write the phrase "A number less 41" as a variable expression using $x$ to represent "a number." 2. The phrase "less" means subtraction, so "a number less 41"

1. **State the problem:** Add and simplify the fractions $\frac{1}{14} + \frac{2}{14} + \frac{8}{14}$. 2. **Formula and rules:** When adding fractions with the same denominator, ad

1. **State the problem:** We need to find the average score of the golf team members: Alice (-11), Ben (-3), Chris (2), Dan (4), Emeril (5), and Fran (9). 2. **Formula for average:

1. **State the problem:** We need to write the rate of residents per county as a unit rate. 2. **Given:** There are 193,116 residents living in 22 counties.

1. **State the problem:** We need to find the number of which 8351 is 126%. 2. **Formula:** If $a$ is $p\%$ of $x$, then $a = \frac{p}{100} \times x$.

1. **State the problem:** Solve the equation $$y + \frac{5}{6} = \frac{1}{6}$$ for $y$. 2. **Formula and rules:** To isolate $y$, subtract $\frac{5}{6}$ from both sides of the equa

1. **State the problem:** Find the least common multiple (LCM) of the numbers 30 and 90. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using the formul

1. **State the problem:** Subtract the fractions $\frac{8}{25} - \frac{5}{25}$ and simplify the result. 2. **Formula and rules:** When subtracting fractions with the same denominat

1. **State the problem:** Crystal skied 18 times and spent a total of 558. We need to find the cost per skiing trip. 2. **Formula used:** To find the cost per trip, use the formula