🧮 algebra

1. The problem is to graph a line using the zero point (0,0) and another point from a given table. 2. To graph a line, you need two points. One point is given as the origin (0,0).

1. **State the problem:** We have a mapping from input values to output values: Input: 7, 8, 10, 14

1. **State the problem:** Solve the inequality $12 \leq 3x - 3 - 2x$. 2. **Simplify the right side:** Combine like terms on the right side.

1. **State the problem:** Solve the inequality $2 + 2x \geq 3x - 1$ for $x$. 2. **Write down the inequality:**

1. **State the problem:** A rectangular lawn measures 8 meters by 4 meters and is surrounded by a flower bed of uniform width $x$ meters. The total area of the lawn plus the flower

1. **State the problem:** Solve the equation $2^x + x = 5$ for $x$. 2. **Understand the equation:** This is a transcendental equation involving both an exponential term $2^x$ and a

1. **State the problem:** You are given the height function of a curved arch support:

1. **State the problem:** Simplify the rational function $$f(x) = \frac{x^3 - x^2 - 12x}{4x^3 - 4x^2 - 8x}$$. 2. **Factor numerator and denominator:**

1. The problem is to classify the given numbers and fractions as integers or non-integers. 2. The numbers given are: 20, 5, \frac{1}{5}, 15%, -10, and 15.

1. **State the problem:** We need to order the temperatures 0°F, 12°F, -15°F, and -8°F from coldest to warmest. 2. **Understand the concept:** On the temperature scale, smaller num

1. **State the problem:** Solve the cubic equation $$ (3x - 4)^3 = 8 $$ 2. **Recall the formula:** To solve an equation of the form $$ (a)^3 = b $$, take the cube root of both side

1. **State the problem:** Solve the equation $ (x+1)(x+3)(x+5)(x+7) = 9 $. 2. **Rewrite the equation:** Notice the terms are symmetric around the middle. Group them as $[(x+1)(x+7)

1. **State the problem:** Multiply the expressions $3x^2$ and $6xy$. 2. **Recall the multiplication rule for algebraic terms:** When multiplying terms with the same base, add their

1. Let's solve the equation $-4 - \frac{2y}{5} = -12$ step-by-step. 2. First, we want to get rid of the $-4$ on the left side to isolate the term with $y$. We do this by adding $4$

1. The problem is to isolate $y$ in the expression $\frac{2y}{5} + 16$. 2. To isolate $y$, we want to get $y$ alone on one side of the equation.

1. **State the problem:** Evaluate the expressions: 1) $\left(\sqrt[3]{64}\right)^2$

1. The problem asks what is true about the function on the interval $-4 < x < -1$. 2. From the graph description, on the interval $-4 < x < -1$, the function is part of the linear

1. **State the problem:** We need to find the interval where the function is both increasing and linear. 2. **Analyze the graph description:** The function has three parts:

1. The problem asks to translate the phrase "22 increased by twice Gail's age" into an algebraic expression. 2. We use the variable $g$ to represent Gail's age.

1. **Problem:** Find all possible roots of the radicals given. 2. **Recall:** The nth root of a real number $a$ is written as $$\sqrt[n]{a}$$. If no index is shown, it is assumed t

1. The problem asks for the end behavior of the function $y = f(x)$ based on the graph description. 2. End behavior describes how the function behaves as $x \to \infty$ (far right)