🧮 algebra

1. Problem: Find the H.C.F of $6x$ and $3y$. 2. Factor each monomial into numeric primes and variable factors: $6x = 2\cdot 3\cdot x$ and $3y = 3\cdot y$.

1. **State the problem:** Factor the expression $tw + 10t - 2w - 20$. 2. **Group terms:** Group the terms to factor by grouping:

1. The problem is to simplify the expression $\frac{79}{22}$.\n\n2. Since 79 and 22 have no common factors other than 1, the fraction is already in its simplest form.\n\n3. Therefo

1. Statement of the problem. Solve the equation $4x = 20$.

1. The problem states that Boone County has 858 to spend on new street signs, and each sign costs 26. 2. We need to find how many signs the county can buy with 858.

1. The problem is to simplify the expression $x + 5$. 2. Since $x + 5$ is already in its simplest form, no further simplification is needed.

1. The problem is to solve the equation $4x = 20$ for $x$. 2. To isolate $x$, divide both sides of the equation by 4:

1. **Find** $(2x + 9)^2$. This means we need to square the binomial. 2. Use the formula for squaring a binomial: $$(a + b)^2 = a^2 + 2ab + b^2$$

1. **State the problem:** Solve for $x$ in the equation $$x - 14 = 20$$

1. **State the problem:** Solve for $x$ in the equation $$4x = 20.$$\n\n2. **Isolate the variable:** To solve for $x$, divide both sides of the equation by 4 to get $$x = \frac{20}

1. The problem is to solve for the variable $x$ in the equation: $$x + 13 = 27$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{28} = \frac{9}{7}$$. 2. **Understand the equation:** This is a proportion where two fractions are equal.

Problem: Solve for the variable x in the equation $\frac{x}{28} = \frac{9}{7}$. 1. Multiply both sides by 28 to isolate x.

1. Find the sum of $(4x + 2y - 6z) + (5y - 2z + 7x) + (-9z - 2x - 3y)$. Combine like terms:

1. **Problem a:** Determine if the point $(-3,4)$ lies on the line given by the equation $$y + 3x + 2 = 0.$$ 2. Substitute $x = -3$ and $y = 4$ into the line equation:

1. The problem is to express the number $7.5 \times 10^{-2}$ in decimal form. 2. Recall that $10^{-2}$ means $\frac{1}{10^2} = \frac{1}{100} = 0.01$.

1. The problem is to evaluate the expression $7.5 \times 10^{-2}$. 2. Recall that $10^{-2}$ means $\frac{1}{10^2} = \frac{1}{100}$.

1. The problem is to simplify algebraic expressions by adding like terms. 2. Like terms are terms that have the same variables raised to the same powers. Only like terms can be add

1. **State the problem:** Solve the inequality \( \frac{x - 7}{x - 4} > 0 \). 2. **Find critical points:** The numerator is zero at \(x = 7\), and the denominator is zero at \(x =

1. **State the problem:** Find the zeros of the function $$f(x) = 3x^4 - 50x^3 + 124x^2 + 242x + 65$$. The zeros are the values of $x$ for which $f(x) = 0$. 2. **Set the equation t

1. **State the problem:** Solve the inequality $$(x - 2)(x - 4)(x - 5) \geq 0$$ and find the solution set in interval notation. 2. **Identify boundary points:** The factors are zer