🧮 algebra

1. **State the problem:** Solve the equation $X \times X + x\overline{x} = 10$. 2. **Understand the terms:** Here, $X \times X$ means $X^2$.

1. **State the problem:** Solve the equation $3b + 6 - 3b = 9$ for $b$. 2. **Simplify the equation:** Combine like terms on the left side.

1. **State the problem:** Solve the quadratic equation $2x^2 - 8x = 0$ for $x$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the

1. **State the problem:** Simplify the expression $\left(x+\frac{1}{3}\right)\left(x-\frac{1}{3}\right) - \left(-\frac{2}{3} - 2x\right)^2$. 2. **Recall formulas:**

1. **State the problem:** Solve the inequality $$x^3 - 6x^2 + 11x - 6 < 0$$. 2. **Factor the cubic polynomial:** To solve the inequality, first factor the cubic expression. We look

1. The problem is to solve the inequality $-4 > - \frac{4}{3} s$ for $s$. 2. To isolate $s$, first multiply both sides of the inequality by $-1$ to remove the negative signs. Remem

1. **Problem Statement:** We are given a table of time $t$ (in hours) and distance $d$ (in kilometers) for Paul's drive from Vancouver to Kelowna. We need to graph the linear relat

1. The problem is to isolate $y$ by taking 3 away from $y$. 2. The expression can be written as $y - 3$.

1. The problem is to simplify the expression $\frac{57}{8} \div 3$. 2. Recall that dividing by a number is the same as multiplying by its reciprocal. So, $\frac{57}{8} \div 3 = \fr

1. **State the problem:** We are given a set of time and distance data points and told the relationship is linear. We want to find the linear equation relating distance $d$ (km) to

1. **State the problem:** Solve the inequality $$4|4x + 4| + 3 > -7$$. 2. **Understand the absolute value and inequality:** The absolute value expression $$|4x + 4|$$ is always non

1. The problem asks to find the values of $m$ (slope) and $c$ (y-intercept) for the line $T$ given by the equation $y = mx + c$. 2. The slope $m$ of a line passing through two poin

1. Evaluate (a) $\frac{1}{4} + \left(-\frac{3}{4}\right)$ Step 1: Add the fractions with common denominator 4.

1. **State the problem:** Simplify the expression $$\frac{1}{4} \times \left| \left( \frac{3}{2} + \frac{1}{4} \right) \div \sqrt{\frac{49}{4}} - 1 \right|.$$\n\n2. **Recall the ru

1. **Problem:** Add the two matrices: $$\begin{bmatrix}10 & 2 \\ 3 & 7\end{bmatrix} + \begin{bmatrix}-4 & 6 \\ 2 & 10\end{bmatrix}$$

1. The problem is to analyze the function $$f(x) = \frac{1}{3}x^{\frac{4}{3}} - x^{\frac{1}{3}}$$ for $$x \in [0,3]$$. 2. This function involves fractional exponents. Recall that $

1. **State the problem:** Find the equation of the straight line passing through the points $(-5,0)$ and $(0,7)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a li

1. **State the problem:** Calculate the sum of two matrices:

1. **State the problem:** Solve the equation $25j = 14$ for $j$. 2. **Formula and rules:** To solve for $j$, divide both sides of the equation by 25. When dividing both sides by th

1. **State the problem:** Solve the equation $2x + 2 = 48$ for $x$. 2. **Write down the formula and rules:** This is a linear equation. To solve for $x$, isolate $x$ by performing

1. **Stating the problem:** Solve the inequality $$\frac{3x + 5}{2} < 10$$ for $x$.