🧮 algebra

1. **State the problem:** Determine if 7 is a solution to the equation $$7x = 56 - x$$. 2. **Substitute the value:** Replace $$x$$ with 7 in the equation:

1. **State the problem:** Solve the equation $$2x - (-0.3) = 1.9$$. 2. **Rewrite the equation:** Subtracting a negative is the same as adding a positive, so rewrite as:

1. The problem asks if the number 2 is a solution to the equation $3 - p = 1$. 2. Substitute $p = 2$ into the equation to check.

1. The problem asks if the number 2 is a solution to the equation $$3 - p = 1$$. 2. To check, substitute $$p = 2$$ into the equation.

1. The problem asks to write the phrase "A number divided by 60" as a variable expression using $x$ to represent "a number." 2. The phrase "A number divided by 60" means we take th

1. **State the problem:** Solve the equation $$8(y + 6) = 10y + 48$$. 2. **Apply the distributive property:** Multiply 8 by both terms inside the parentheses.

1. **State the problem:** Solve the linear equation $$\frac{1}{3}x + 4 = 2$$. 2. **Isolate the variable term:** Subtract 4 from both sides to get $$\frac{1}{3}x + 4 - 4 = 2 - 4$$ w

1. The problem asks us to write the sentence "The product of -11 and -7 gives 77" as an equation. 2. "Product" means multiplication, so we multiply -11 and -7.

1. **State the problem:** Solve the linear equation $$-\frac{1}{5}r = 2$$ for $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ by undoing the multiplication

1. **State the problem:** Solve the equation $$2c + 5 - c = 14$$ for the variable $c$. 2. **Combine like terms:** On the left side, combine $2c$ and $-c$:

1. The problem is to understand and graph the function $f(x) = \sqrt{x + 2}$. 2. This function is a square root function shifted horizontally. The general form is $f(x) = \sqrt{x -

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

1. **State the problem:** Evaluate the expression $$\frac{xy}{z} + \frac{5}{12}$$ for $$x = -4$$, $$y = -3$$, and $$z = 6$$. 2. **Write the formula and substitute values:**

1. The problem asks to identify the property used to multiply the expression $-3(2x + 1)$. 2. The expression involves multiplying a single term outside the parentheses by each term

1. **State the problem:** Solve the equation $x - 5.7 = 19$ for $x$. 2. **Formula and rules:** To isolate $x$, add $5.7$ to both sides of the equation. This uses the addition prope

1. The problem states: "Six subtracted from a number gives 44." We need to write this as an equation using $x$ to represent "a number." 2. "Six subtracted from a number" means we t

1. The problem asks to write the sentence "The product of 3 and the sum of -69 and a number gives -24" as an equation using $x$ to represent the number. 2. The phrase "product of 3

1. **State the problem:** Solve the equation $$4x - 4 = 5(x - 9)$$. 2. **Apply the distributive property:** Expand the right side:

1. The problem asks to fill in the blank in the sentence: "By the ________ property of equality, we may multiply or divide both sides of an equation by any nonzero number without c

1. The problem asks to write the sentence "The quotient of -112 and 8 amounts to -14" as an equation. 2. The word "quotient" means division, so the quotient of -112 and 8 is writte

1. **State the problem:** Solve the equation $$- \frac{5}{4} x = \frac{10}{20}$$ for $x$. 2. **Simplify the right side:** $$\frac{10}{20} = \frac{1}{2}$$.