🧮 algebra

Let's solve this step by step! 🎉 **Step 1:** Imagine you have apples 🍎 and bananas 🍌 and coconuts 🥥.

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **Problem:** What is the difference between **union** and **intersection** in sets? 2. **Union means “or”:** The union of two sets, written as $A \cup B$, means all elements tha

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We are given two equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$\begin{cases} 2x + y = 8 \\ 2x - y = 12 \end{cases}$$

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We need to find the value of $x$ such that $f(x) = 4$ given the function $f(x) = 2x + 2$. 2. **Write the equation:** Set the function equal to 4:

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the equati

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite division as multiplication:** Dividing by a fraction is the

1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 + 5x} \div \frac{xy + 6x - 5y - 30}{5x - 15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. The problem asks to identify which equations show $y$ in a proportional relationship with $x$. 2. A proportional relationship means $y$ is directly proportional to $x$, which ca

1. **State the problem:** We need to determine if each statement about unit rates is true or false. 2. **Recall the formula for unit rate:** The unit rate of a ratio $\frac{a}{b} :

1. **State the problem:** Two kittens together weigh 3 1/4 pounds. We want to find possible individual weights for each kitten. 2. **Convert mixed number to improper fraction:** 3

1. **State the problem:** Find the total weight in ounces of the three kittens that weigh the least. 2. **Identify the weights of the kittens:** From the line plot, the kitten weig

1. **State the problem:** We have two towns, A and B, with populations growing exponentially. Town A starts with 4000 people and grows at 8% per year. Town B starts with 5000 peopl

1. **Simplify** $\frac{\sqrt{3} - 5\sqrt{2}}{5\sqrt{3}}$. Use the property $\frac{a - b}{c} = \frac{a}{c} - \frac{b}{c}$:

1. The problem involves simplifying an expression with $m$ in the denominator, specifically $m^{5/2}$. 2. Recall the rule for exponents: when dividing powers with the same base, su

1. **State the problem:** Simplify the expression $$\left(\frac{64m^{1/2}r^3}{m^{3/2}r^{1/4}}\right)^{1/2}$$ and find which of the given options is equivalent. 2. **Recall the rule

1. **State the problem:** Solve the system of equations: $$5x + 4y = -14$$