Solving Algebraic Equations

Questions and Answers

What is the simplified form of the numerator in the given equation?

$y - 6y$ (correct)

$y - (-y)$

$y + y$

$y - 15y$

What is the simplified form of the denominator in the given equation?

$2y$

$10y$

$6y$ (correct)

$20y$

What is the final simplified form of the equation $\frac{(y - (7 - 8)y)}{(9y - (3 + 4)y)} = \frac{2}{3}$ ?

$\frac{2y}{6y} = \frac{2}{3}$

$\frac{y}{y} = \frac{2}{3}$

$\frac{2y}{x} = \frac{2}{3}$

$\frac{2y}{2y} = \frac{2}{3}$ (correct)

Solving the simplified equation, what is the value of $y$?

$y = \infty$ Signup and view all the answers

Which form below correctly represents the simplified value of the numerator?

$2y$ Signup and view all the answers

What is the simplified form of the expression $7 - 8$?

-1 Signup and view all the answers

What does the expression $(3 - 4y)^2$ expand to?

9 - 24y + 16y^2 Signup and view all the answers

Simplify $y - (-1)y$.

2y Signup and view all the answers

What is the simplified form of the denominator $9y$?

9y Signup and view all the answers

What is $-2/9$ when the common terms are factorized?

-2/9 Signup and view all the answers

What is the first step in solving the equation $\frac{x}{4} + \frac{3}{2} = \frac{5}{8}$?

Subtract $\frac{3}{2}$ from both sides. Signup and view all the answers

After subtracting $\frac{3}{2}$ from both sides, what is the resulting equation?

$\frac{x}{4} = \frac{-19}{8}$ Signup and view all the answers

What is the next step after obtaining $\frac{x}{4} = \frac{-7}{8}$?

Multiply both sides by 4. Signup and view all the answers

What is the value of x when $\frac{x}{4} = \frac{-7}{8}$?

$\frac{-7}{2}$ Signup and view all the answers

Which of the following checks the solution x of $\frac{x}{4} + \frac{3}{2} = \frac{5}{8}$?

$\frac{-7}{8} + \frac{12}{8} = \frac{5}{8}$ Signup and view all the answers

What is the simplified form of the left-hand side of the equation?

$\frac{-7y}{9y-3y}$ Signup and view all the answers

What is the correct representation of the numerator of the left-hand expression?

$y - (2 - 8)y$ Signup and view all the answers

What is the correct representation of the denominator of the left-hand expression?

$9y - (3 - 4y)$ Signup and view all the answers

What is the result when the left-hand side of the equation is simplified?

$\frac{-7}{6}$ Signup and view all the answers

What is the value of $y$ that satisfies the equation?

$-2$ Signup and view all the answers

What is the value of $4 - (3 - 9)$?

10 Signup and view all the answers

What is the result of $2 - 8$?

-6 Signup and view all the answers

What is the simplified value of $\frac{-6}{10}$?

$-\frac{3}{5}$ Signup and view all the answers

What is the numerator in the simplified form of the expression $\frac{2 - 8}{4 - (3 - 9)}$?

-6 Signup and view all the answers

What is the correct simplified form of the expression $\frac{2 - 8}{10}$?

$-\frac{3}{5}$ Signup and view all the answers

What is the simplified form of the numerator of the expression?

-8y + y Signup and view all the answers

What is the simplified form of the denominator of the expression?

9y - (3 - 4y)^2 Signup and view all the answers

How do you simplify $(3 - 4y)^2$?

$9 - 24y + 16y^2$ Signup and view all the answers

What is the final simplified form of $rac{y - (7 - 8)y}{9y - (3 - 4y)^2}$?

$rac{7y}{25y^2 - 24y + 9}$ Signup and view all the answers

What values of $y$ satisfy the equality $rac{7y}{25y^2 - 24y + 9} = rac{2}{3}$?

$y = -rac{3}{2}$ Signup and view all the answers

What is the simplified form of the numerator $y - (7 - 8y)$?

$-7 + 9y$ Signup and view all the answers

What is the simplified form of the denominator $9y - (6 + 4y)$?

$9y - 6 - 4y$ Signup and view all the answers

What is the final simplified form of the fraction before solving for $y$?

$\frac{-7 + 9y}{5y - 6}$ Signup and view all the answers

What is the first step to solve the equation $\frac{-7 + 9y}{5y - 6} = \frac{2}{3}$?

Cross multiply Signup and view all the answers

After cross multiplying, which equation do you get?

$2(-7 + 9y) = 3(5y - 6)$ Signup and view all the answers

What is the first step in solving the equation $\frac{y-(7-8y)}{9y-(3+4y)}=\frac{2}{3}$?

Cross multiply to eliminate the fraction Signup and view all the answers

After cross-multiplying, what does the equation $\frac{y-(7-8y)}{9y-(3+4y)}=\frac{2}{3}$ become?

$3(y - 7 + 8y) = 2(9y - 3 - 4y)$ Signup and view all the answers

What is the simplified form of $y-(7-8y)$?

$9y - 7$ Signup and view all the answers

If $\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}$ is simplified further, what does $9y - (3 + 4y)$ become?

$5y - 3$ Signup and view all the answers

After simplifying and solving $\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}$, what is the value of $y$?

$y = \frac{1}{3}$ Signup and view all the answers

What is the simplified form of the expression $y - (7 - 8y)$?

$8y - 7$ Signup and view all the answers

What is the simplified form of the expression $9y - (3 - 4y)$?

$9y - 3 + 4y$ Signup and view all the answers

What is the combined simplified form of the denominator $9y - 3 + 4y$?

$13y - 3$ Signup and view all the answers

After simplifying the equation to $rac{8y - 7}{13y - 3} = rac{2}{3}$, what should the next step be to solve for $y$?

Cross multiply to get $3(8y - 7) = 2(13y - 3)$ Signup and view all the answers

What is the final value of $y$ after solving $3(8y - 7) = 2(13y - 3)$?

$y = 1$ Signup and view all the answers

What is the first step to simplify the expression in the numerator $y - (7 - 8y)$?

Distribute the negative sign across the parentheses. Signup and view all the answers

What does the expression $y - (7 - 8y)$ simplify to?

9y - 7 Signup and view all the answers

What is the correct expansion of $(3 + 4y)^2$?

$9 + 24y + 16y^2$ Signup and view all the answers

After simplifying the fraction on the left side of the equation, what is the denominator?

$-9 + 24y - 16y^2$ Signup and view all the answers

What value of $y$ solves the equation $\frac{(9y - 7)}{(-9 + 24y - 16y^2)} = \frac{2}{3}$?