🧮 algebra

1. **State the problem:** We need to find the values of $x$ that satisfy the equation $$(3x - 1)(x - 5) = 0$$. 2. **Recall the zero product property:** If the product of two factor

1. **State the problem:** Solve the quadratic equation $$12 - 8w + w^2 = 0$$. 2. **Rewrite the equation in standard form:** The standard form of a quadratic equation is $$aw^2 + bw

1. **State the problem:** Factor the trinomial $$5x^2 + 29x + 20$$. 2. **Recall the factoring method for trinomials:** For a quadratic in the form $$ax^2 + bx + c$$, we look for tw

1. **State the problem:** Factor the trinomial $$2x^2 + 5x + 3$$. 2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two numbers that mul

1. **State the problem:** Solve the quadratic equation $$z^2 + 10z + 15 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$az^2 + bz + c = 0$

1. **State the problem:** We have a pattern of tile arrays where for each step $s$, the array is a rectangle of size $s \times (s+1)$. We want to find the number of tiles when $s =

1. **State the problem:** We want to find how many tiles there will be when $s = 10$ in the pattern where the number of tiles forms a rectangle of size $s$ by $(s+1)$. 2. **Identif

1. **State the problem:** Solve the system of equations using the substitution method: $$x + 2y = 6$$

1. **State the problem:** We need to find the equation of a line with slope $m = -9$ passing through the point $(5, -2)$ in slope-intercept form $y = mx + b$. 2. **Recall the formu

1. Solve for $x$: $$2x + 5 = 15$$ 2. Factor the quadratic expression: $$x^2 + 5x + 6$$

1. **State the problem:** We need to add the fractions $\frac{5}{8}$ and $\frac{1}{16}$ and express the result in its simplest form. 2. **Find a common denominator:** The denominat

1. **State the problem:** Solve the linear equation $2x + 5 = 7$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtrac

1. **State the problem:** Factor the expression $$9x^2 - 49$$ completely. 2. **Recognize the form:** This is a difference of squares because $$9x^2 = (3x)^2$$ and $$49 = 7^2$$.

1. **State the problem:** Factor the expression $$1 - 64x^2$$ completely. 2. **Recognize the formula:** This is a difference of squares, which follows the rule:

1. **State the problem:** Factor the expression $$81 - 16x^2$$ completely. 2. **Recognize the formula:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a

1. **State the problem:** Factor the expression $$100 - 121x^2$$ completely. 2. **Recognize the form:** This is a difference of squares because $$100 = 10^2$$ and $$121x^2 = (11x)^

1. **State the problem:** Factor the expression $$x^2 - 64$$ completely. 2. **Recognize the formula:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a -

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

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

1. **State the problem:** We are given the equation $$y - 10 = 2(x - 8)$$ and need to simplify it or express it in a more standard form.

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