Solving Algebraic Equations
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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 $y$?

<p>$y = \infty$ (C)</p> Signup and view all the answers

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

<p>$2y$ (D)</p> Signup and view all the answers

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

<p>-1 (A)</p> Signup and view all the answers

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

<p>9 - 24y + 16y^2 (A)</p> Signup and view all the answers

Simplify $y - (-1)y$.

<p>2y (A)</p> Signup and view all the answers

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

<p>9y (B)</p> Signup and view all the answers

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

<p>-2/9 (D)</p> Signup and view all the answers

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

<p>Subtract $\frac{3}{2}$ from both sides. (B)</p> Signup and view all the answers

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

<p>$\frac{x}{4} = \frac{-19}{8}$ (B)</p> Signup and view all the answers

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

<p>Multiply both sides by 4. (B)</p> Signup and view all the answers

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

<p>$\frac{-7}{2}$ (C)</p> Signup and view all the answers

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

<p>$\frac{-7}{8} + \frac{12}{8} = \frac{5}{8}$ (D)</p> Signup and view all the answers

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

<p>$\frac{-7y}{9y-3y}$ (C)</p> Signup and view all the answers

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

<p>$y - (2 - 8)y$ (C)</p> Signup and view all the answers

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

<p>$9y - (3 - 4y)$ (B)</p> Signup and view all the answers

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

<p>$\frac{-7}{6}$ (D)</p> Signup and view all the answers

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

<p>$-2$ (A)</p> Signup and view all the answers

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

<p>10 (A)</p> Signup and view all the answers

What is the result of $2 - 8$?

<p>-6 (D)</p> Signup and view all the answers

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

<p>$-\frac{3}{5}$ (C)</p> Signup and view all the answers

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

<p>-6 (D)</p> Signup and view all the answers

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

<p>$-\frac{3}{5}$ (C)</p> Signup and view all the answers

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

<p>-8y + y (B)</p> Signup and view all the answers

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

<p>9y - (3 - 4y)^2 (A)</p> Signup and view all the answers

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

<p>$9 - 24y + 16y^2$ (B)</p> Signup and view all the answers

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

<p>$rac{7y}{25y^2 - 24y + 9}$ (B)</p> Signup and view all the answers

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

<p>$y = -rac{3}{2}$ (C)</p> Signup and view all the answers

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

<p>$-7 + 9y$ (A)</p> Signup and view all the answers

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

<p>$9y - 6 - 4y$ (D)</p> Signup and view all the answers

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

<p>$\frac{-7 + 9y}{5y - 6}$ (A)</p> Signup and view all the answers

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

<p>Cross multiply (B)</p> Signup and view all the answers

After cross multiplying, which equation do you get?

<p>$2(-7 + 9y) = 3(5y - 6)$ (A)</p> Signup and view all the answers

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

<p>Cross multiply to eliminate the fraction (D)</p> Signup and view all the answers

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

<p>$3(y - 7 + 8y) = 2(9y - 3 - 4y)$ (A), $3(y - 7 + 8y) = 2(9y - 3 - 4y)$ (B)</p> Signup and view all the answers

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

<p>$9y - 7$ (A)</p> 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?

<p>$5y - 3$ (D)</p> 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 $y$?

<p>$y = \frac{1}{3}$ (A)</p> Signup and view all the answers

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

<p>$8y - 7$ (A)</p> Signup and view all the answers

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

<p>$9y - 3 + 4y$ (C)</p> Signup and view all the answers

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

<p>$13y - 3$ (A)</p> 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 $y$?

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

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

<p>$y = 1$ (D)</p> Signup and view all the answers

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

<p>Distribute the negative sign across the parentheses. (C)</p> Signup and view all the answers

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

<p>9y - 7 (C)</p> Signup and view all the answers

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

<p>$9 + 24y + 16y^2$ (C)</p> Signup and view all the answers

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

<p>$-9 + 24y - 16y^2$ (C)</p> Signup and view all the answers

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

<p>$y = 1$ (A)</p> Signup and view all the answers

Study Notes

Simplifying Algebraic Expressions

  • The given expression is y = (7 - 8)y - 2 / 9y - (3 - 4y)^2, which can be rewritten in different forms.
  • Another form of the expression is y - (7 - 8)y / 9y - (3 - 4)y = 2 / 3.
  • The expression can also be written as y - (7 - 8)y / 9y - (3 + 4)y = 2 / 3.
  • The expression y - (7 - 8)y / 9y - (6 + 4)y = 2 / 3 is also an equivalent form.
  • The expression y - (7 - 8)y / 9y - (3 - 4)y^2 = 2 / 3 is another way to rewrite the original expression.

Evaluating Expressions

  • The expression y = (2 - 8) / (4 - (3 - 9)) can be simplified to y = (2 - 8) / (4 + 6).
  • Further simplification leads to y = (-6) / 10, which equals -3 / 5.
  • Therefore, the final simplified value of y is -3 / 5.

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Solve the algebraic equation involving multiple variables and operations. Practice your algebra skills with this challenging equation.

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