🧮 algebra

1. The problem is to solve the equation $\frac{c}{15} = 3$ for $c$. 2. The formula used here is to isolate $c$ by multiplying both sides of the equation by 15 to cancel the denomin

1. **State the problem:** Reggie spends a total of $22.25 at the movie theater, which includes the cost of his ticket plus $10.25 for popcorn and soda. We need to find the cost $c$

1. **State the problem:** We are given two linear equations: $$y = \frac{1}{3}x + 2$$

1. The problem is to find the vertex of the quadratic function $$y = - (x + 4)^2 - 4$$. 2. The vertex form of a quadratic function is $$y = a(x - h)^2 + k$$, where $$(h, k)$$ is th

1. **State the problem:** We are given the function $$y = (x - 5)^2 + 1$$ and asked to find the coordinates of its vertex. 2. **Recall the vertex form of a parabola:** The function

1. The problem states that Victor and his friends raised a total of $79.25 over two days. 2. On the second day, they raised $64.25.

1. **State the problem:** Solve the equation $\frac{1}{2} - \frac{1}{3}p = \frac{3}{4}$ for $p$. 2. **Isolate the term with $p$:** Subtract $\frac{1}{2}$ from both sides:

1. The problem asks: Which equation can you use to find the cost $c$ of each costume if two costumes cost 25 in total? 2. We know the total cost of two costumes is 25, so the sum o

1. **State the problem:** Simplify the expression $\frac{1}{2} - 1$. 2. **Recall the rule:** To subtract a whole number from a fraction, convert the whole number to a fraction with

1. The problem asks to "do the same for all of them," but since no specific problems are provided, I will demonstrate solving a typical algebraic equation as an example. 2. Conside

1. **State the problem:** Solve the equation $$\frac{4}{5}x + 3 = -\frac{7}{10}$$ for $x$. 2. **Isolate the term with $x$:** Subtract 3 from both sides:

1. **State the problem:** Melissa spent 29 on a calculator and 3 each for notebooks. We want to find an expression for her total cost if she buys $x$ notebooks.

1. **Problem (b):** Simplify the expression $$(2w^3 - 4 - 8w - 3w^2 + w^6) + (w^2 - w - 2)$$ 2. **Step 1:** Write the expression grouping like terms:

1. **State the problem:** There are initially more boys than girls in a hall. Specifically, there are 5 more boys than girls.

1. **Stating the problem:** We have two sequences given:

1. **State the problem:** Simplify the expressions $\sqrt{112}$, $\sqrt{63}$, and then find the sum $\sqrt{112} + \sqrt{63}$.\n\n2. **Recall the formula and rules:** The square roo

1. **State the problem:** Simplify the expression $$(\sqrt{x} + 5)(\sqrt{x} - 3)$$. 2. **Recall the formula:** This is a product of two binomials, which can be expanded using the d

1. **State the problem:** Simplify the expression $2y + 9y(5x + 6b)3x + 7b$. 2. **Apply the distributive property:** First, multiply $9y$ by the expression $(5x + 6b)$ and then mul

1. **State the problem:** Solve for $x$ in the equation $$\log_3(3x - 2) = 2.$$\n\n2. **Recall the logarithm definition:** The equation $\log_a b = c$ means $$a^c = b.$$\n\n3. **Ap

1. **State the problem:** Solve for $x$ in the equation $\log_6 36 = 5x + 3$. 2. **Recall the logarithm definition:** $\log_a b = c$ means $a^c = b$.

1. **State the problem:** Solve the inequality $$1.39 > \frac{z}{7}$$ for $z$. 2. **Recall the rule:** To isolate $z$, multiply both sides of the inequality by 7. Since 7 is positi