🧮 algebra

1. You asked to explain the previous math problem in a simpler way. 2. To simplify explanations, we use easy words and break down each step clearly.

1. **State the problem:** Liam’s current salary is 76000. He will receive a 5% increase on 1 July and then another 5% increase on 1 January. We need to find his new salary from 1 J

1. **State the problem:** Solve the equation $$\frac{x+\frac{1}{2}}{x-\frac{1}{3}} = \frac{3}{2}$$ for $x$. 2. **Rewrite the equation:** To simplify, write the numerator and denomi

1. **State the problem:** Simplify the expression $$\left( \frac{16x^{5}y^{10}}{81xy^{2}} \right)^{\frac{3}{4}}$$ assuming all variables are positive. 2. **Simplify inside the pare

1. **Simplify the expression:** $64 - 9\sqrt{4}$. 2. **State the problem:** We need to simplify $64 - 9\sqrt{4}$.

1. **State the problem:** Solve for $x$ in the equation $$4.8 \times 10^3 = 2x^2 (0.0100 - x)(0.0200 + x).$$ 2. **Rewrite the equation:**

1. The problem asks to classify each of the five expressions as functions or not functions. 2. Recall that a function assigns exactly one output for each input.

1. State the problem: Label the top-center number line which runs from -4 to 4 and has a red filled circle at 3. 2. Formula and notation: The relevant expressions to consider are $

1. Let's clarify step 6 where 8 was added instead of subtracted. 2. Usually, when solving equations, the operation depends on the equation's structure and what maintains equality.

1. **State the problem:** Simplify and evaluate the expression $$\left(-5 - 2(8 - 4 \times 3)\right)^2 \times 0$$. 2. **Apply order of operations (PEMDAS):** Parentheses, Exponents

1. Let's clarify the problem: You want to know how to find the values of $a$ and $b$ in a given context, usually from an equation or data. 2. Typically, $a$ and $b$ are parameters

1. The problem asks to find the vertex of each quadratic function using the formula for the x-coordinate of the vertex: $$x = -\frac{b}{2a}$$ where the quadratic is in the form $$y

1. **State the problem:** Frank buys candy at 8 per pound and will spend at most 96 on candy. We want to find the possible number of pounds $p$ he can buy. 2. **Write the inequalit

1. **State the problem:** Solve the inequality $-17 - 4x > -37$ for $x$. 2. **Isolate the variable term:** Add 17 to both sides to move the constant term on the left side.

1. The problem is to simplify the fraction $\frac{5}{12}$. 2. The formula for simplifying a fraction is to divide the numerator and denominator by their greatest common divisor (GC

1. **State the problem:** We need to find the number $x$ such that 60 is $\frac{6}{12}$ of $x$. 2. **Write the equation:** Since 60 is $\frac{6}{12}$ of $x$, we write:

1. **State the problem:** We need to analyze and graph the function $$y = |x| - |x - 1|$$. 2. **Recall the definition of absolute value:** For any real number $a$, $$|a| = \begin{c

1. **State the problem:** Find the coordinates of the midpoint of the line segment joining the points $(4, -11)$ and $(-2, 7)$. 2. **Formula for midpoint:** The midpoint $M$ of a l

1. **Problem statement:** Given that one root of the quadratic equation $x^2 - 3x + a = 0$ is $x=6$, find the value of $a$ and the other root. 2. **Formula and rules:** For a quadr

1. **State the problem:** We want to find the order size $x$ that minimizes the cost per unit, given the total cost function $$C(x) = 5x^2 + 320.$$ 2. **Define cost per unit:** The

1. **State the problem:** Simplify the expression $$a^2 (2a + 5a^3 + 1) - 10a$$. 2. **Apply the distributive property:** Multiply $$a^2$$ by each term inside the parentheses: