🧮 algebra

1. The problem is to evaluate the expression $3(-3)$. 2. This is a multiplication problem where a positive number is multiplied by a negative number.

1. **State the problem:** Evaluate the expression $-2(0)$. 2. **Recall the multiplication rule:** Any number multiplied by zero equals zero.

1. The problem is to solve the equation $|2^x| = 2^9$. 2. Since $2^x$ is always positive for any real $x$, the absolute value does not change the expression. So, $|2^x| = 2^x$.

1. **Problem statement:** Given that $a, b, c$ are in arithmetic sequence (A.P.) and $x, y, z$ are in geometric sequence (G.P.), prove that $$(x^{b-c})(y^{c-a})(z^{a-b}) = 1.$$ 2.

1. The problem is to understand the four laws of radicals, which are rules for simplifying expressions involving roots. 2. The first law is the Product Rule: $$\sqrt[n]{a} \times \

1. The problem is to check all intersections and verify the numbers given, not just those that prefer one option. 2. To find intersections of functions or values, we set them equal

1. Stating the problem: Solve the equation $3^{x-2} = \left(\frac{1}{3}\right)^{-2x}$ for $x$. 2. Recall the property of exponents: $\left(\frac{1}{a}\right)^b = a^{-b}$.

1. **State the problem:** Solve the equation $3^x = 61.25$ for $x$. 2. **Recall the formula:** To solve for $x$ in an exponential equation $a^x = b$, use logarithms: $x = \log_a b$

1. **State the problem:** Solve the equation $2x + 3 = 11$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **Stating the problem:** We need to solve equation 3 in the same way as equation 9, following the steps and instructions provided.

1. **State the problem:** Factor the cubic polynomial $x^3 + x^2 - 4x - 4$ using the factor theorem. 2. **Recall the factor theorem:** If $f(a) = 0$ for some number $a$, then $(x -

1. **State the problem:** Solve the system of equations: $$x + y = 10$$

1. The problem is to graph the inequality $y + 3x > -2$. 2. First, rewrite the inequality in terms of $y$ to make it easier to graph:

1. **State the problem:** Solve for $h$ in the equation $$\frac{h}{6} - 1 = -3$$. 2. **Add 1 to both sides** to isolate the term with $h$:

1. The problem is to analyze the linear equation $y = 5x$. 2. This is a linear function where $y$ depends on $x$ with a slope of 5 and a y-intercept of 0.

1. **State the problem:** Solve the system of equations: $$x - 4y = 8$$

1. The problem is to understand how to graph points on the Cartesian plane and interpret their positions. 2. The Cartesian plane consists of two perpendicular number lines: the x-a

1. **State the problem:** Solve for $x$ in the equation $\sqrt{3x} = 15$. 2. **Formula and rules:** To solve for $x$, we need to eliminate the square root by squaring both sides of

1. Problem: Rewrite the expression $2x + 7 + 3x - 2 + 3$ by combining like terms. 2. Formula: Combine like terms by adding or subtracting coefficients of the same variable and cons

1. **State the problem:** Solve the system of linear equations: $$x - 4y = 8$$

1. The problem is to solve the function $f(x) = x^2$. 2. This function represents a parabola opening upwards with vertex at the origin $(0,0)$.