🧮 algebra

1. **State the problem:** Factor the expression $$18x^2 - 3$$ completely. 2. **Identify the GCF (Greatest Common Factor):** The terms are $$18x^2$$ and $$-3$$.

1. **State the problem:** We need to find the slope of a line perpendicular to the line given by the equation $$4x - 6y = -60$$. 2. **Rewrite the equation in slope-intercept form:*

1. **State the problem:** We need to find the slope of a line perpendicular to the line given by the equation $$x - y = 3$$. 2. **Rewrite the equation in slope-intercept form:** Th

1. **State the problem:** We need to find an expression for the perimeter of the shape by summing all given side lengths and then simplify the expression. 2. **Write the perimeter

1. **State the problem:** Simplify the algebraic expression $3bp + 5pw + 7pb + 4bw + 2wp$ by combining like terms. 2. **Identify like terms:** Note that multiplication is commutati

1. **State the problem:** Simplify the expression $$3dg + 6d + 2gr + 4gd + 7d$$ by combining like terms. 2. **Identify like terms:** Terms with the same variables multiplied togeth

1. **State the problem:** We need to find a linear model of the form $$y = mx + b$$ that fits the given data points: $$x: 4, 7, 10, 13, 16, 19$$

1. **State the problem:** We need to find the linear function $y = mx + b$ that best fits the given data points $(1,7), (3,12), (5,17), (7,22), (9,27)$. 2. **Formula for linear reg

1. **State the problem:** Solve the simultaneous equations: $$2y^2 + x^2 = -6x + 42$$

1. **State the problem:** Solve for $k$ in the equation $$k + \frac{6}{9} = -\frac{8}{3}$$. 2. **Simplify fractions:** Note that $\frac{6}{9}$ can be reduced by dividing numerator

1. **State the problem:** You want to graph the solution of the inequality $x < -7$ on a number line. 2. **Draw a horizontal line:** This line represents all real numbers.

1. **State the problem:** Solve the inequality $$2x + 16 < 2$$ and represent the solution on a number line. 2. **Write the inequality:** $$2x + 16 < 2$$

1. **State the problem:** Solve for $c$ in the equation $$10 + c^2 = 74$$. 2. **Isolate the variable term:** Subtract $10$ from both sides to isolate $c^2$:

1. **State the problem:** Solve the equation $$\frac{7}{3}m + 6 + \frac{1}{3}m + 14 = 5\left(\frac{1}{3}m + 2\right)$$ for $m$. 2. **Combine like terms on the left side:**

1. **State the problem:** Solve the equation $$11 - 6c + 3(4 + c) = 5(5 - c) - 3c$$ for the variable $$c$$. 2. **Apply the distributive property:** Expand the terms with parenthese

1. **State the problem:** Solve the equation $$e^{\frac{x^3}{4}} = 2$$ for $x$. 2. **Recall the formula and rules:** The natural exponential function $e^y$ is one-to-one, so if $e^

1. **State the problem:** Solve the equation $$2n - 9 + 2n + 1 = 17 - n$$ for the variable $$n$$. 2. **Combine like terms on the left side:**

1. **State the problem:** Solve the equation $$\frac{3m}{5} = \frac{5m - 4}{10}$$ for $m$. 2. **Use the cross-multiplication formula:** When two fractions are equal, their cross pr

1. **State the problem:** We need to find the value(s) of $x$ such that $f(x) = g(x)$ where $f(x) = \frac{x-2}{-2}$ and $g(x) = -4x + 24$. 2. **Set the functions equal:** To find $

1. **State the problem:** We need to find the solution(s) to the equation $$f(x) = g(x)$$ where $$f(x) = (x+1)^3 - 1$$ and $$g(x) = - \frac{3}{4} x - \frac{3}{14}$$ by graphing bot

1. **State the problem:** We need to determine if each piecewise function $f(x)$, $h(x)$, and $g(x)$ has a range of $(-\infty,4)$. This means the output values of the function cove