🧮 algebra

1. **State the problem:** Solve the linear equation $$-8x + 1 = 17$$ for $x$. 2. **Isolate the variable term:** Subtract 1 from both sides to get rid of the constant on the left.

1. **State the problem:** Solve the linear equation $$-5x - 7 = 13$$ for $$x$$. 2. **Write the formula and rules:** To solve for $$x$$, isolate $$x$$ by performing inverse operatio

1. **State the problem:** We need to simplify the product $ (2 + \sqrt{7})(2 + \sqrt{7}) $. 2. **Formula used:** When multiplying two binomials of the form $(a + b)(a + b)$, we use

1. **State the problem:** Simplify the product $\left(\sqrt{5} + 6\right)\left(\sqrt{5} - 6\right)$.\n\n2. **Formula used:** This is a product of conjugates, which follows the diff

1. The problem is to simplify the expression $$\sqrt{25x^3}$$ assuming $$x > 0$$. 2. Recall the property of square roots: $$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$$.

1. **State the problem:** Simplify the expression $$\sqrt{19x^{13}}$$ assuming $$x > 0$$. 2. **Recall the property of radicals:** $$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$$ and $$\s

1. The problem asks to simplify the expression \(\sqrt{25x}\) assuming \(x > 0\). 2. Recall the property of square roots: \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\).

1. **State the problem:** Simplify the expression $$\sqrt{25x^4}$$ assuming $$x > 0$$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $

1. **State the problem:** Simplify the expression $$x^2\sqrt{x^2}$$ assuming $$x > 0$$. 2. **Recall the properties:** The square root of $$x^2$$ is $$|x|$$, but since $$x > 0$$, $$

1. The problem asks to compare the y-intercepts and rates of change of two functions. 2. The first function is given as $y = 6x - 1$.

1. **State the problem:** Compare the y-intercepts and rates of change (slopes) of the line given by the equation $y = 1.2x + 0.4$ and the line passing through the points $(3,4)$ a

1. **State the problem:** Find the slope of the line passing through the points $(3, 8)$ and $(6, 7)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $

1. **State the problem:** Find the slope of the line passing through the points $(1, 9)$ and $(8, 8)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $

1. **Problem stated:** Make a one-page cheat sheet from the pages about **slope, slope-intercept form, graphing linear equations, functions, and relations**. 2. **Key formulas to k

1. **State the problem:** Simplify the expression $(x+9)(x-8)$. 2. **Use the distributive property (FOIL method) for binomials:**

1. **State the problem:** Simplify the expression $$\frac{32x}{x^2 + x - 72} \div \frac{16x - 8}{2x^2 - 17x + 8}$$

1. **State the problem:** Solve the equation $x^2 - 32 = -4x$ for all values of $x$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equ

1. **State the problem:** Solve the quadratic equation $$x^2 - 12x + 35 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation o

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x = 35$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of the

1. **State the problem:** We want to rewrite the quadratic equation $$-6x^2 - 582 = -60x$$ in the form $$(x + a)^2 = b$$ by completing the square. 2. **Rewrite the equation:** Move

1. **State the problem:** Complete the square for the quadratic equation $$-6x^2 - 582 = -60x$$ and write it in the form $$(x + a)^2 = b$$. 2. **Rewrite the equation:** Move all te