🧮 algebra

1. **State the problem:** Solve the equation $$-4(z - 12) = 42$$ for the variable $$z$$. 2. **Use the distributive property:** Multiply $$-4$$ by each term inside the parentheses.

1. **State the problem:** Simplify the fraction $$\frac{(3t^{-1})^{-3}}{4t^{7}j}$$ so that all exponents are positive. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{(3t^{-1})^{-3}}{4t^{7}j}$$ so that it contains only positive exponents. 2. **Recall the exponent rules:**

1. **Problem:** Solve for $h$ in the formula $$S = 2\pi r(r + h)$$ 2. **Formula:** The surface area $S$ of a cylinder is given by $$S = 2\pi r(r + h)$$ where $r$ is the radius and

1. **State the problem:** We need to order the given mathematical expressions from least to greatest. 2. **Evaluate each expression:**

1. **State the problem:** Simplify or expand the expression $$b -7x^2(1 - x)^3$$. 2. **Recall the binomial expansion formula:** For any binomial $$(a - b)^3 = a^3 - 3a^2b + 3ab^2 -

1. **State the problem:** Simplify the expression $$2(f^4)^2 f^2$$ and express the answer with only positive exponents. 2. **Recall the exponent rules:**

1. **State the problem:** We need to evaluate the expression $$2x^0 - 3x$$ when $$x = 4$$. 2. **Recall the rules:** Any number raised to the power of zero is 1, so $$x^0 = 1$$ for

1. The problem asks: What does the slope mean? 2. The slope is a measure of how steep a line is on a graph.

1. **State the problem:** Find the slope of the line passing through the points $(0, 10)$ and $(24, 6)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. The problem asks to turn a statement or expression into an equation. 2. An equation is a mathematical statement that asserts the equality of two expressions, typically written a

1. **State the problem:** Rodrick worked 37.5 hours and earned 346.88 before taxes. We need to find his hourly wage. 2. **Formula:** Hourly wage $= \frac{\text{Total pay}}{\text{Ho

1. **State the problem:** A farmer wants to build a fence around a rectangular pen that is $16$ feet long. The area of the pen is $80$ square feet. We need to determine if $40$ fee

1. **State the problem:** We need to solve the equation $$2x + 5 = 17$$ for the variable $x$. 2. **Isolate the term with $x$:** To solve for $x$, we first want to get rid of the co

1. **State the problem:** We need to solve the system of simultaneous equations: $$2x + y = 7$$

1. **State the problem:** We need to solve for the variable $x$ in an equation. 2. **General approach:** To solve for $x$, isolate $x$ on one side of the equation using algebraic o

1. **State the problem:** We are given three expressions representing the sides of a figure: $3x+8$, $5x+2$, and $7x-4$. We need to find the perimeter, which is the sum of all side

1. **Stel het probleem vast:** Vereenvoudig de uitdrukking $$\frac{-2P^{-2}}{Y^{-\frac{1}{2}}+P^{-2}}$$. 2. **Gebruik de regels voor negatieve exponenten:**

1. The problem is to find the value of $\sqrt{100}$. 2. The square root function $\sqrt{x}$ gives a number which, when multiplied by itself, equals $x$.

1. **State the problem:** Find the value of the expression $$[ -4^2 + (3 - 5)^3 - (-5) ] - [ |-3|^2 + 2 - 2^3 ]$$ using the order of operations.

1. **State the problem:** Solve the two-step equation $$- \frac{1}{2} = \frac{1}{5} w - \frac{1}{3}$$ for $w$. 2. **Add $\frac{1}{3}$ to both sides** to isolate the term with $w$: