🧮 algebra

1. **State the problem:** Simplify the expression $1 - 1$. 2. **Recall the subtraction rule:** Subtracting a number from itself results in zero.

1. **State the problem:** We have two classes selling raffle tickets at different prices and amounts already raised. We want to find the equation to determine $t$, the number of ti

1. **State the problem:** We want to find the number of years $x$ it will take for Jerry and Victoria to earn the same salary given their starting salaries and annual increases.

1. **State the problem:** We need to determine which inequality is true among the given options involving $x$: - $30x < 330 + 50x$

1. **State the problem:** We have a rectangle with width $3$ units and an unknown length $L$ units. The problem states that the perimeter and the area of the rectangle have the sam

1. **State the problem:** Julie started with 20 pieces of gum and gave away $x$ pieces. Conrad started with 35 pieces and gave away twice as many as Julie, which is $2x$ pieces. We

1. Solve $3^2 - 2^3 = 1$. Calculate powers: $3^2 = 9$, $2^3 = 8$.

1. The problem asks us to find the ordered pair that is a solution to both linear equations represented by the two lines on the graph. 2. A solution to a system of linear equations

1. **Problem Statement:** We are given two lines represented by linear equations graphed on a coordinate grid. We need to find which ordered pair from the options is a solution to

1. The problem asks for the x-coordinate of the ordered pair that is the solution to the system of two linear equations represented by the two lines on the graph. 2. The solution t

1. **State the problem:** We need to find which ordered pair from the options a, b, c, d is a solution to both linear equations represented by the two lines. 2. **Find the equation

1. Problem: For each pair of functions, identify one characteristic they share and one characteristic that distinguishes them. 2. Pair a) $f(x) = \frac{1}{x}$ and $g(x) = x$:

1. **State the problem:** Simplify the expression $$\frac{1}{4} - \frac{1}{2} + \frac{1}{3} + \frac{2}{3}$$. 2. **Find a common denominator:** The denominators are 4, 2, and 3. The

1. The problem is to simplify the expression \(\log x \cdot \log x\).\n\n2. Recall that multiplying a quantity by itself is the same as squaring it. So, \(\log x \cdot \log x = (\l

1. The problem asks to find the domain of two functions: (a) $f(x) = \sqrt{x} + 2$ and (b) $g(x) = \frac{1}{x^2 - x}$.\n\n2. For function (a), the domain is all $x$ values for whic

1. **Stating the problem:** We are given the linear function $y = 2x + 3$ and asked to find the value of $y$ when $x = 2$. 2. **Formula used:** The function is already given as $y

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. Problem 1: Given $f(x) = \frac{(1+2x)^2}{1-x^2}$ (i) Find the first 4 terms in the power series expansion.

1. Problem (a): Rationalize and simplify the expression $$\frac{\sqrt{10}}{\sqrt{5} - 2}$$. 2. To rationalize the denominator, multiply numerator and denominator by the conjugate o