🧮 algebra

1. **State the problem:** Simplify the expression $3\sqrt{7} + 6\sqrt{7}$. 2. **Identify like terms:** Both terms contain $\sqrt{7}$, so they are like terms and can be combined by

1. **State the problem:** Write an equation in slope-intercept form of the line that passes through the points $(-2, 3)$ and $(2, 7)$. 2. **Recall the formula for slope:** The slop

1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$

1. **State the problem:** Solve the inequality $$5x + 7 < 26$$ and find the solution set for $$x$$. 2. **Formula and rules:** To solve a two-step inequality, first isolate the vari

1. **State the problem:** Factor completely the expression $$7(3x + 2)^2 (x - 1)^2 + (3x + 2)(x - 1)^3$$ and simplify as much as possible. 2. **Identify common factors:** Both term

1. **State the problem:** Solve the inequality $5 + 7x < 26$ for $x$. 2. **Isolate the variable term:** Subtract 5 from both sides to get the term with $x$ alone.

1. Solve the system of equations by graphing: $$y - \frac{1}{4}x = -1$$

1. **Problem statement:** We have a photograph of dimensions 8 inches by 12 inches inside a frame of width $x$ inches around all sides. We want to find a function $A(x)$ that repre

1. **State the problem:** We need to find the area of a rectangle with sides labeled $x - 3$ and $x + 3$. 2. **Formula for area of a rectangle:**

1. **State the problem:** Simplify the expression using the distributive property: $$\frac{1}{4}(12 + 16v)$$ 2. **Recall the distributive property:** For any numbers $a$, $b$, and

1. **State the problem:** Simplify the expression $(2ba)^4$ using the power of a power rule. 2. **Recall the power of a power rule:** When raising a product to a power, raise each

1. **State the problem:** Solve for the variable $s$ in the equation $8 + s = 14$. 2. **Formula and rules:** To isolate $s$, subtract 8 from both sides of the equation. This uses t

1. The problem asks to find the equivalent decimal and percent for the fraction $\frac{5}{4}$.\n\n2. To convert a fraction to a decimal, divide the numerator by the denominator: $$

1. **State the problem:** Use the distributive property to remove the parentheses in the expression $ (w + 2) 2 $. 2. **Recall the distributive property:** The distributive propert

1. **State the problem:** Solve the inequality $$4 \geq -7j - 6 \geq -10$$ for the variable $j$. 2. **Rewrite the compound inequality:** This means we have two inequalities to solv

1. **State the problem:** Solve the compound inequality $$\frac{3t + 1}{2} \geq -1 \text{ or } t + 14 \leq 8$$ for $t$ and write the answer as a compound inequality with integers.

1. **Stating the problem:** We have the following function compositions and equalities:

1. **State the problem:** Find the approximate monthly percent change for the function $f(t) = 16(1.4)^t$ which models the number of deer after $t$ years. 2. **Recall the yearly gr

1. The problem is to expand the expression $4(x + 3)$ using the Distributive Property. 2. The Distributive Property states that $a(b + c) = ab + ac$. This means you multiply the te

1. The problem involves understanding the composition of operators $r_l$ and $r_m$ acting on elements $F$, $G$, and $B$ with given relations: $$r_l \circ r_m (F) = G$$

1. **State the problem:** Find the approximate monthly percent change for the function $f(t) = 16(1.4)^t$ which models the number of deer after $t$ years. 2. **Recall the yearly gr