🧮 algebra

1. **State the problem:** Solve the absolute value inequality $$\frac{2|x - 5|}{7} \geq 10$$ and find the values of $x$ such that $x \geq ?$ and $x \leq ?$. 2. **Isolate the absolu

1. **State the problem:** Solve the absolute value equation $$|x - 8| + 1 = 11$$ for $x$. 2. **Isolate the absolute value:** Subtract 1 from both sides:

1. **State the problem:** Solve the absolute value equation $$\frac{|10|x + 8||}{5} = 24$$ for $x$. 2. **Simplify the expression inside the absolute value:** Note that $|10| = 10$,

1. The problem is to find the remainder when one number or polynomial is divided by another. 2. For integers, use the division algorithm: if you divide $a$ by $b$, the remainder $r

1. **State the problem:** Solve the compound inequality \( \frac{m - 2}{3} \leq -4 \) OR \( 3m - 8 > 4 \). 2. **Solve the first inequality:**

1. **State the problem:** Solve the compound inequality \(m - \frac{2}{3} \leq -4\) OR \(3m - 8 > 4\). 2. **Solve the first inequality:**

1. The problem involves understanding and graphing the system of inequalities: $$y \leq x + 2$$

1. **State the problem:** We are given that the shaded region satisfies the inequality $y \geq 1$ and we need to find the other two inequalities from the options A to E that define

1. The problem is to identify the system of inequalities that define the yellow shaded triangular region on the graph. 2. The graph shows three lines:

1. The problem is to multiply two hexadecimal numbers: 2B78 and 3A. 2. Convert each hexadecimal number to decimal.

1. **State the problem:** We need to verify the calculations of the Refund Rate and Aftersale Rate based on the given totals. 2. **Given data:**

1. The problem is to simplify or factor the quadratic expression $x^2 + 6x + 9$. 2. Recognize that this is a quadratic trinomial and check if it can be factored as a perfect square

1. We are asked to solve the quadratic equation $x^2 + 6x + 1 = 0$. 2. To solve this, we use the quadratic formula:

1. The problem is to multiply the hexadecimal numbers 1B0D8 and 9A. 2. Convert each hexadecimal number to decimal for easier multiplication.

1. The problem is to find the sum of two hexadecimal numbers. 2. Hexadecimal numbers use base 16, with digits 0-9 and letters A-F representing values 10-15.

1. **State the problem:** We need to sketch the graph of the function $$y = 2(x - 2)^3 + 1$$ and understand its behavior. 2. **Identify the base function:** The base function is $$

1. Consider the function $y = (2x + 3)(x - 1)(x - 4)$. (a) Find the x-intercepts by setting $y=0$:

1. **Simplify the expression** $\sqrt{2} \times \sqrt{4} \times \sqrt{8} \div \sqrt{2}$. Recall that $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$, so:

1. **State the problem:** We need to find the percentage of the grain's weight lost after drying, given the moisture content before and after drying. 2. **Define variables:** Let t

1. The problem is to find 17% of 453. 2. To find a percentage of a number, convert the percentage to a decimal by dividing by 100: $$17\% = \frac{17}{100} = 0.17$$.

1. The problem asks which values of $m$ are possible given the graph. 2. The graph shows a filled circle at $m = -3$ and an arrow pointing left, indicating $m \leq -3$.