🧮 algebra

1. **Problem:** Solve the equation $2x+3=11$. 2. **Goal:** Isolate $x$ by undoing operations in reverse order.

1. **State the problem:** Solve the equation $-x + \frac{3y}{2} = 10 - 2x$ for $y$ in terms of $x$. 2. **Rewrite the equation:**

1. **Problem 1:** Beth walks 4 km to the station at 6 km/h and wants to catch the 0924 bus. Find the latest time she can leave home. 2. Calculate the time taken to walk 4 km at 6 k

1. **State the problem:** We are given a linear relationship between $t$ and $\log_4 V$ for $t \geq 0$ with the line $l$ passing through $(0, \log_4 40000)$ and having gradient $-\

1. The problem states that all buses take the same time to travel from the station to the city centre. 2. We are given the departure times from the station: 09:24 and 11:06.

1. Problem: Convert each given linear equation to slope-intercept form $y = mx + b$ and interpret the slope and intercept. 2. For $11\ 2x = \frac{5x - 2y}{4}$:

1. **Problem statement:** (b) Express $ (2 + x)^{-1} $ in the form $ A(1 + Bx)^{-1} $ where $ A $ and $ B $ are rational numbers.

1. Given equation: $3x - 2y = 15$ Rewrite in slope-intercept form $y = mx + b$:

1. Stating the problem: Solve the equation $X + \frac{2y}{2} = -6$ for $X$ in terms of $y$. 2. Simplify the fraction: $\frac{2y}{2} = y$.

1. The problem asks for the equation of a line with gradient $\frac{2}{5}$ and y-intercept at $(0, -5)$ in the form $ax + by = c$ where $a$, $b$, and $c$ are integers in lowest ter

1. **Problem statement:** The value of a car $V$ is modeled by $V = ab^t$, where $a$ and $b$ are constants and $t$ is the number of years since purchase. The line $l$ shows the lin

1. **State the problem:** We need to determine the slope of the line segment that passes through the points approximately $(-5, 7)$ and $(6, -6)$. 2. **Recall the slope formula:**

1. **State the problem:** We need to determine the slope of the line passing through the points $(-7, -7)$ and $(7, 7)$. 2. **Recall the slope formula:** The slope $m$ of a line pa

1. **State the problem:** Find the slope of the line passing through the points (0, -4) and (1, -6). 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$

1. The problem states that Hulu produces 20% of its own original shows and there are 500 shows available in total. 2. To find the number of original shows, we calculate 20% of 500.

1. The problem is to find the lowest common denominator (LCD) of the fractions $\frac{9}{20}$ and $\frac{8}{15}$.\n\n2. The denominators are 20 and 15. We need to find the least co

1. The problem asks us to find the value of the fraction $$\frac{59049}{729}$$ using the given table of powers of 9. 2. From the table, we see that $$59049 = 9^5$$ and $$729 = 9^3$

1. State the problem: Calculate $\left(9.3 \times 10^{-4}\right) \div \left(3 \times 10^{2}\right) + \left(5.2 \times 10^{-7}\right)$ and express the answer in standard form. 2. Di

1. **State the problem:** Calculate $\left(6 \times 10^4\right)^2 - \left(4 \times 10^8\right)$ and express the answer in standard form. 2. **Square the first term:**

1. The problem states that the input 6 first goes through an addition operation "+ 8" and then the result is divided by 2. 2. Start by adding 8 to the input 6:

1. The problem states that an input number goes through two operations: first, 3 is added to it, then the result is multiplied by 4, and the final output is 20. 2. Let the input be