🧮 algebra

1. **State the problem:** We need to find the equation of a line that is parallel to the line $2x - 3y = -4$ and passes through the point $(-5, 3)$. 2. **Recall the formula and rul

1. **State the problem:** Find the equation of a line with $x$-intercept $2$ and passing through the point $(4,-5)$. 2. **Recall the formula:** The $x$-intercept means the line cro

1. **State the problem:** Find the equation of a line with $x$-intercept $2$ and passing through the point $(4,-5)$. 2. **Recall the formula:** The $x$-intercept means the line cro

1. **State the problem:** We are given functions and asked to evaluate or find compositions of functions for given values or expressions.

1. **State the problem:** Solve the equation $$-2x + 0.5(3x + 10) = -1.1 - (5.5x + 5)$$ for $x$. 2. **Distribute and simplify both sides:**

1. **Problem 65:** Divide $c^3 - 3c^2 + 18c - 16$ by $c^2 + 3c - 2$ using long division. 2. **Step 1:** Write the division setup:

1. **State the problem:** Solve for $c$ in the equation $$-\frac{5}{6} = \frac{1}{2} - \frac{2}{3} c$$. 2. **Isolate the term with $c$:** Subtract $\frac{1}{2}$ from both sides:

1. **State the problem:** Solve the equation $$-\frac{1}{2} x + 3 = -5 - \frac{1}{2} (9x + 1)$$ for $x$ and simplify the answer. 2. **Distribute and simplify:** Apply the distribut

1. **State the problem:** Solve the linear equation $$-5 + 2x = 5 - (-9x - 4) - 5x$$ for $x$. 2. **Apply the distributive property:** Remove the parentheses on the right side by di

1. **State the problem:** Solve the equation $$-5 + 2x = 5 - (-9x - 4) - 5x$$ for $x$. 2. **Apply the distributive property and simplify inside the parentheses:**

1. **State the problem:** Solve the equation $$3x + 8 = 5x + 22$$ for $$x$$. 2. **Write down the formula and rules:** To solve for $$x$$, we want to isolate $$x$$ on one side of th

1. **State the problem:** Solve the equation $$-(-5.2x + 6) - 6.2x = -1$$ for $$x$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the negative sig

1. **State the problem:** Solve for $z$ in the equation $$\frac{5}{12} z + \frac{1}{4} = -\frac{1}{4}$$. 2. **Isolate the term with $z$:** Subtract $\frac{1}{4}$ from both sides:

1. **State the problem:** Solve the equation $$-10x + 3(3x + 4) + 1 = -3(7x + 3)$$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $$5x - 2(0.1x - 1) = 7.2 - 4.4(-x - 6)$$ for $$x$$. 2. **Apply the distributive property:**

1. **State the problem:** Solve for $b$ in the equation $$-\frac{5}{8} = -\frac{1}{2} + \frac{3}{4} b$$. 2. **Isolate the term with $b$:** Add $\frac{1}{2}$ to both sides to move t

1. The problem is to determine if it is valid (licit) to change logarithms of any base into natural logarithms (base $e$) before solving. 2. The key formula used is the change of b

1. **State the problem:** We want to solve the exponential equation $$3^{2x} = 75$$ for $x$. 2. **Recall the logarithm definition:** Logarithms are the inverse operations of expone

1. **State the problem:** Solve the inequality $$|4x| \geq -7$$ and graph the solution set. 2. **Recall the property of absolute values:** The absolute value of any real number is

1. **State the problem:** We are given a system of three linear equations:

1. **State the problem:** Simplify the expression $$16x^2 + 32 + 15$$. 2. **Combine like terms:** The terms $$32$$ and $$15$$ are constants and can be added together.