🧮 algebra

1. For the linear equation $y = 3 - 4x$: - The equation is already in slope-intercept form $y = mx + b$ where $m$ is the gradient and $b$ is the y-intercept.

1. **State the problem:** Solve the inequality $$-2(4 + 3x) > 7$$ and express the solution in interval notation. 2. **Distribute the -2:**

1. **State the problem:** We are given the equation $$V = \frac{1}{U} + \frac{1}{W}$$ and asked to solve for $U$. 2. **Isolate the term with $U$:** Start by subtracting $$\frac{1}{

1. The problem is to solve for $U$ in an equation where $U$ is the unknown variable. 2. Since the equation is not provided, let's consider a general approach: isolate $U$ on one si

1. The problem is to understand and analyze the equation $$\frac{1}{V} = \frac{1}{U} + \frac{1}{W}$$ which relates three variables $V$, $U$, and $W$. 2. This equation can be interp

1. **State the problem:** The tide starts 20 meters from the shore and recedes at a rate of 3 meters per hour for 6 hours. 2. **Identify what is asked:** Find the distance of the t

1. **State the problem:** We are given a point $a(-4,1)$ and a slope $m=\frac{2}{3}$. We want to find the $y$-coordinate of point $b$ when $x=8$ on the line passing through $a$ wit

1. Let's analyze the expression $(-c^3)^2$. When raising a power to another power, we multiply the exponents:

1. **State the problem:** Solve the equation $$3 |3x - 7| - 1 = 6x + 20$$ for $x$. 2. **Isolate the absolute value:** Add 1 to both sides:

1. Solve the equation $\frac{1}{3}(x+1) = \frac{1}{2}(x-2)$. Multiply both sides by 6 (the least common multiple of 3 and 2) to clear denominators:

1. **Problem statement:** Simplify each expression by applying the power of a product rule and the power of a power rule. 2. **Part a:** Simplify $ (3 m^4)^2 $.

1. The problem is to understand and simplify the function $f(x) = 5\sqrt{x} + 10$. 2. Here, $\sqrt{x}$ means the square root of $x$, which is the number that when multiplied by its

1. The problem is to analyze the function $f(x) = 5$. 2. This is a constant function, meaning for every value of $x$, the output is always 5.

1. **State the problem:** The temperature in a freezer increased from $-23$ degrees Celsius to $3$ degrees Celsius over $2$ hours. We need to find the average change in temperature

1. The problem is to simplify the expressions $(3m^4)^2$ and $(2n^5)^3$. 2. For $(3m^4)^2$, we apply the power of a product rule: $(ab)^n = a^n b^n$.

1. সমস্যাটি হলো: $(4x^3 - x)^2$ এর উৎপাদক বিশ্লেষণ করা। 2. প্রথমে, আমরা $(a - b)^2 = a^2 - 2ab + b^2$ সূত্রটি ব্যবহার করব, যেখানে $a = 4x^3$ এবং $b = x$।

1. The problem is to simplify the expression $$(4x^3 - x)^2$$. 2. Recognize that this is a square of a binomial, which can be expanded using the formula $$(a - b)^2 = a^2 - 2ab + b

1. **State the problem:** Simplify the expression $$(4x^3 - x)^2$$. 2. **Apply the square of a binomial formula:** Recall that $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. The problem is to simplify the expression $$(4x^3 - 2)^2$$. 2. Recall that squaring a binomial means multiplying it by itself: $$(4x^3 - 2)^2 = (4x^3 - 2)(4x^3 - 2)$$.

1. The problem asks to simplify the expressions $(3m^4)^2$ and $(2n^5)^3$ using exponent rules. 2. For $(3m^4)^2$, apply the power of a product rule: $(ab)^n = a^n b^n$.

1. **State the problem:** The water level in a well was initially 65 meters below the ground surface. After 5 days of rain, it rose to 30 meters below the ground surface. We need t