🧮 algebra

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 $x$.

1. **State the problem:** Simplify the expression $$\left( \frac{3a^2 b^3}{cd} \right)^3 \div \left( \frac{3ab^4}{c^2 d^3} \right)^2$$. 2. **Recall the rules:**

1. **State the problem:** We need to expand and simplify the expression $$(4x-11)(-x+2)$$. 2. **Recall the distributive property:** To multiply two binomials, multiply each term in

1. **State the problem:** Perform the polynomial long division of $$2x^4 + 3x^3 + 3x^2 - 5x - 3$$ by $$2x^2 - x - 1$$. 2. **Recall the division process:** Divide the leading term o

1. **State the problem:** Simplify the expression $$\left(\frac{2xy^{5}}{z^{2}}\right)^3 \cdot \left(\frac{x z^{3}}{y}\right)^4$$. 2. **Recall the power of a quotient rule:** For a

1. **State the problem:** Solve for $n$ in the equation $$\frac{3n+1}{5} - \frac{7-5n}{3} = \frac{5}{6}.$$\n\n2. **Identify the formula and rules:** To solve equations with fractio

1. **State the problem:** Solve the equation $X + 4 = 21$ for $X$. 2. **Formula and rule:** To isolate $X$, subtract 4 from both sides of the equation. This uses the subtraction pr

1. **State the problem:** Solve for $n$ in the equation $\left(32+\frac{1}{5}\right)-\left(7-\frac{5n}{3}\right)=\frac{5}{6}$.\n\n2. **Rewrite the equation:** \n$$32 + \frac{1}{5}