🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$\frac{29}{36}x + 120 = x.$$\n\n2. **Isolate the variable terms:** Subtract $\frac{29}{36}x$ from both sides to get all $x$

1. **State the problem:** We need to solve the expression $$\frac{29}{36} + 120$$. 2. **Convert the whole number to a fraction:** To add a fraction and a whole number, express the

1. **Solve the system:** $$\frac{2}{x} + \frac{2}{3y} = \frac{1}{6}, \quad \frac{3}{x} + \frac{2}{y} = 0$$

1. The problem involves simplifying the expression $$\frac{1}{4} \times \frac{5}{9} \times 120$$. 2. First, multiply the numerators and denominators of the fractions: $$\frac{1 \ti

1. The problem asks to find the result of the integral, but the expressions given are unclear as written. Let's interpret the left and right columns as separate expressions to simp

1. **State the problem:** We are given two equations: $$x^2 - y^2 = 30$$

1. To answer "Where did the six come from?", I need to know the specific problem or equation you are referring to. 2. The number six could appear as a coefficient, constant, or res

1. **State the problem:** We are given two equations: $$x^2 - y^2 = 30$$

1. **State the problem:** We are given two equations: $$x^2 - y^2 = 30$$

1. **State the problem:** Expand and simplify the expression $$(3p - 7)(4p - 8)$$. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parenthesis

1. Stating the problem: Solve the equation $$\frac{x+5}{4} = \frac{(5-3x)2 + 4}{5}$$ for $x$. 2. Simplify the right side numerator: $$(5-3x)2 + 4 = 2(5-3x) + 4 = 10 - 6x + 4 = 14 -

1. Stating the problem: Solve the equation $x + \frac{5}{4} = \frac{(5 - 3x)2 + 4}{5}$ for $x$. 2. Simplify the right side numerator: $(5 - 3x)2 + 4 = 2(5 - 3x) + 4 = 10 - 6x + 4 =

1. **State the problem:** Expand and fully simplify the expression $$(2x + 5)(4x - 3)(5x - 4)$$ to write it in the form $$ax^3 + bx^2 + cx + d$$ and find the values of $$a, b, c,$$

1. **State the problem:** Determine if the point $(3, -1)$ satisfies the system of inequalities represented by the shaded regions on the graph. 2. **Identify the lines and inequali

1. The problem asks if the point $(-4,4)$ satisfies the system of inequalities represented by two lines: - A blue line with an upward slope, shading above it.

1. **State the problem:** Determine if the point $(-2, -3)$ satisfies the system of inequalities represented by the two lines and their shaded regions. 2. **Identify the inequaliti

1. **State the problem:** We need to determine if the point $(-1,7)$ satisfies the system of inequalities: $$2x + 5y > -6$$

1. The problem asks if the point $(1, 5)$ is a solution to the system of inequalities represented by the graph. 2. The graph has two boundary lines:

1. **State the problem:** We need to solve the system of inequalities graphically:

1. The problem is to simplify the expression $\log 3 - \log 4$. 2. Recall the logarithm property: $\log a - \log b = \log \left( \frac{a}{b} \right)$.

1. The problem is to simplify the expression $\sqrt{2}$.\n\n2. The square root of 2, written as $\sqrt{2}$, is an irrational number and cannot be simplified further into a simpler