🧮 algebra

1. The problem is to simplify the expression $(6 - (-8)) \div (-7)$.\n\n2. First, simplify inside the parentheses: subtracting a negative is the same as adding a positive, so $6 -

1. **State the problem:** Simplify the expression $(-6)^2 \div 4$. 2. **Recall the order of operations:** Exponents are evaluated before division.

1. The problem is to simplify the expression $(–6 – –8)3$. 2. First, simplify inside the parentheses: $–6 – –8$ means $–6 + 8$ because subtracting a negative is the same as adding.

1. The problem is to simplify the expression $-3 + 1 - (-2)$.\n\n2. Recall that subtracting a negative number is the same as adding its positive counterpart. So, $- (-2) = +2$.\n\n

1. **State the problem:** Simplify the expression $2 - 4 \div 4$. 2. **Recall the order of operations:** Division and multiplication are performed before addition and subtraction.

1. **State the problem:** Evaluate the expression $4 + \frac{6^2}{(6 - 2^2)}$. 2. **Recall the order of operations:** Calculate exponents first, then parentheses, then division, an

1. Stating the problem: Simplify the expression $5x2(5x)2$. 2. Understand the expression: The expression can be interpreted as $5 \times 2 \times (5x) \times 2$.

1. **State the problem:** Simplify the expression $(-3x)^3$. 2. **Recall the formula:** When raising a product to a power, use the rule $$(ab)^n = a^n b^n$$ where $a$ and $b$ are f

1. **State the problem:** Simplify the expression $$\frac{3 - x}{6} - \frac{2x}{9}$$. 2. **Find a common denominator:** The denominators are 6 and 9. The least common denominator (

1. Problem: Find the inverse of the function $f(x) = 3x + 7$. 2. To find the inverse, replace $f(x)$ with $y$:

1. **State the problem:** We are given the equation $a = 3(2m - 4)$ and values for $a$ and $m$ in one year: $a = 19$ and $m = 6$. We want to check if these values satisfy the equat

1. **State the problem:** Simplify the expression $2(2+6b) - 3(4b-2)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Factorise the expression $7y(5x+10)-(x+2)(3x+5)$. 2. **Expand each term:**

1. Problem: Simplify the expression $7y(5x+10)-(x+2)(3x+5)$. 2. Formula and rules: use the distributive property $a(b+c)=ab+ac$ and the rule for subtracting an entire expression $-

1. **State the problem:** Solve the equation $\log_{x+8}(3x^2 + 8x) = 2$ for $x$. 2. **Recall the logarithm definition:** $\log_a b = c$ means $a^c = b$, where $a > 0$, $a \neq 1$,

1. **State the problem:** Solve the equation $\log_x(8x - 12) = 2$ for $x$. 2. **Rewrite the logarithmic equation in exponential form:** Recall that $\log_a b = c$ means $a^c = b$.

1. **State the problem:** Solve for all values of $x$ in the equation $$\log_{x+3}(3x^2 + 1) = 2.$$\n\n2. **Recall the logarithm definition:** The equation $\log_a b = c$ means $$a

1. **State the problem:** Solve the logarithmic equation $$\log_2(x^2 - 9x + 4) = 2$$ for all values of $x$. 2. **Recall the logarithm definition:** If $$\log_b(A) = C$$, then $$A

1. **State the problem:** Solve for all values of $x$ in the equation $$\log_5(4x^2 - 1) - \log_5(4x + 2) = 0.$$\n\n2. **Recall the logarithm property:** The difference of logarith

1. **Problem statement:** Expand and simplify the expression $6(3y + 2) + 3(y - 3)$. 2. **Formula and rule:** Use the distributive law: $a(b + c) = ab + ac$. This means multiply ea

1. **State the problem:** Solve for $x$ in the equation $$\log_2(x^2 + 7) - \log_2(x + 5) = 3.$$\n\n2. **Recall the logarithm subtraction rule:** $$\log_b A - \log_b B = \log_b \le