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Algebra 1 : Variables

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Example Questions

Example Question #32 : Binomials

Solve for $\displaystyle x$ in terms of $\displaystyle y$:

$\frac{4}{3}x-3=\frac{2}{9}y$ $\displaystyle \frac{4}{3}x-3=\frac{2}{9}y$

Possible Answers:

$x=\frac{-8}{27}y+3$ $\displaystyle x=\frac{-8}{27}y+3$

$x=\frac{1}{6}y+\frac{9}{4}$ $\displaystyle x=\frac{1}{6}y+\frac{9}{4}$

$x=\frac{8}{27}y+3$ $\displaystyle x=\frac{8}{27}y+3$

$x=\frac{8}{27}y-3$ $\displaystyle x=\frac{8}{27}y-3$

$x=\frac{1}{6}y-\frac{9}{4}$ $\displaystyle x=\frac{1}{6}y-\frac{9}{4}$

Correct answer:

$x=\frac{1}{6}y+\frac{9}{4}$ $\displaystyle x=\frac{1}{6}y+\frac{9}{4}$

Explanation:

First, isolate X onto one side of the equation:

$\frac{4}{3}X-3=\frac{2}{9}Y$ $\displaystyle \frac{4}{3}X-3=\frac{2}{9}Y$

$\displaystyle +3$ $\displaystyle +3$

$\frac{4}{3}X=\frac{2}{9}Y+3$ $\displaystyle \frac{4}{3}X=\frac{2}{9}Y+3$

Next, divide both sides of the equation by 4/3:

$\frac{4}{3}\div \frac{4}{3}X=\frac{4}{3}\div \frac{2}{9}Y+\frac{4}{3}\div \frac{3}{1}$ $\displaystyle \frac{4}{3}\div \frac{4}{3}X=\frac{4}{3}\div \frac{2}{9}Y+\frac{4}{3}\div \frac{3}{1}$

$\frac{3}{4}\cdot \frac{4}{3}X=\frac{3}{4}\cdot \frac{2}{9}Y+\frac{3}{4}\cdot \frac{3}{1}$ $\displaystyle \frac{3}{4}\cdot \frac{4}{3}X=\frac{3}{4}\cdot \frac{2}{9}Y+\frac{3}{4}\cdot \frac{3}{1}$

$X=\frac{6}{36}Y+\frac{9}{4}$ $\displaystyle X=\frac{6}{36}Y+\frac{9}{4}$

When simplified, your answer should be:

$X=\frac{1}{6}Y+\frac{9}{4}$ $\displaystyle X=\frac{1}{6}Y+\frac{9}{4}$

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Example Question #301 : Variables

Solve for $\displaystyle x$

$\displaystyle -1 = 6 + x$

Possible Answers:

$\displaystyle 5$

$\displaystyle 0$

$\displaystyle -5$

$\displaystyle 7$

$\displaystyle -7$

Correct answer:

$\displaystyle -7$

Explanation:

$\displaystyle -1 = 6 + x$

$\displaystyle -1-6 = 6+x-6$

-7 = x $\displaystyle -7 = x$

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Example Question #302 : Variables

Solve for $\displaystyle x$

$\displaystyle 3 = -6 + x$

Possible Answers:

$\displaystyle 3$

$\displaystyle 9$

$\displaystyle -3$

$\displaystyle -2$

$\displaystyle -9$

Correct answer:

$\displaystyle 9$

Explanation:

$\\3 = -6 + x \\3 + 6 = -6 + x + 6 \\9 = x$ $\displaystyle \\3 = -6 + x \\3 + 6 = -6 + x + 6 \\9 = x$

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Example Question #303 : Variables

Solve for $\displaystyle x$

$\displaystyle 3 = 2 - x$

Possible Answers:

$\displaystyle 1$

None of the other answers.

$\displaystyle -5$

$\displaystyle 5$

$\displaystyle -1$

Correct answer:

$\displaystyle -1$

Explanation:

$\\3 = 2 - x \\3 - 2 = 2 - x - 2\\ 1 = -x(-1) = x$ $\displaystyle \\3 = 2 - x \\3 - 2 = 2 - x - 2\\ 1 = -x(-1) = x$

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Example Question #304 : Variables

Solve for $\displaystyle x$

$\displaystyle 19 = 7 + x$

Possible Answers:

$\displaystyle 7$

$\displaystyle -12$

$\displaystyle 12$

$\displaystyle -26$

$\displaystyle 26$

Correct answer:

$\displaystyle 12$

Explanation:

$\\19 = 7 + x \\ 19 - 7 = 7 + x -7 \\ 12 = x$ $\displaystyle \\19 = 7 + x \\ 19 - 7 = 7 + x -7 \\ 12 = x$

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Example Question #305 : Variables

Solve for $\displaystyle x.$

$\displaystyle -9 = 82 + x$

Possible Answers:

$\displaystyle 72$

None of the other answers.

$\displaystyle 73$

$\displaystyle 91$

$\displaystyle -91$

Correct answer:

$\displaystyle -91$

Explanation:

$\\-9 = 82 + x \\ -9 - 82 = 82 + x - 82 \\-91 = x$ $\displaystyle \\-9 = 82 + x \\ -9 - 82 = 82 + x - 82 \\-91 = x$

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Example Question #306 : Variables

Solve for $\displaystyle x$

$\displaystyle 1 = -3 + x$

Possible Answers:

$\displaystyle 0$

$\displaystyle 3$

$\displaystyle 4$

None of the other answers.

$\displaystyle 1$

Correct answer:

$\displaystyle 4$

Explanation:

$\\1 = -3 + x \\1 + 3 = -3 + x + 3\\ 4 = x$ $\displaystyle \\1 = -3 + x \\1 + 3 = -3 + x + 3\\ 4 = x$

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Example Question #4 : Solving Rational Expressions

Simplify:

$\frac{2x-3}{3-2x}$ $\displaystyle \frac{2x-3}{3-2x}$

Possible Answers:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\displaystyle 0$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\displaystyle 1$

$\displaystyle -1$

Correct answer:

$\displaystyle -1$

Explanation:

Factor out $\displaystyle -1$ from the numerator which gives us

$\left -(3-2x \right )$ $\displaystyle \left -(3-2x \right )$

Hence we get the following

$\frac{\left -(3-2x \right )}{3-2x}$ $\displaystyle \frac{\left -(3-2x \right )}{3-2x}$

which is equal to $\displaystyle -1$

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Example Question #1 : Factoring Rational Expressions

Simplify:

$\frac{x+3}{x^{2}+6x+9}$ $\displaystyle \frac{x+3}{x^{2}+6x+9}$

Possible Answers:

$\left ( x-3 \right )$ $\displaystyle \left ( x-3 \right )$

$\frac{1}{x+3}$ $\displaystyle \frac{1}{x+3}$

$\left ( x+3 \right )$ $\displaystyle \left ( x+3 \right )$

$\left ( x+3 \right )^{2}$ $\displaystyle \left ( x+3 \right )^{2}$

$\frac{1}{\left ( x+3 \right )^{2}}$ $\displaystyle \frac{1}{\left ( x+3 \right )^{2}}$

Correct answer:

$\frac{1}{x+3}$ $\displaystyle \frac{1}{x+3}$

Explanation:

If we factors the denominator we get

$\left ( x+3 \right )^{2}$ $\displaystyle \left ( x+3 \right )^{2}$

Hence the rational expression becomes equal to

$\frac{\left ( x+3 \right )}{\left ( x+3 \right )^{2}}$ $\displaystyle \frac{\left ( x+3 \right )}{\left ( x+3 \right )^{2}}$

which is equal to $\frac{1}{\left ( x+3 \right )}$ $\displaystyle \frac{1}{\left ( x+3 \right )}$

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Example Question #307 : Variables

Which of the following fractions is NOT equivalent to $- \frac{x-5}{2x + 3}$ $\displaystyle - \frac{x-5}{2x + 3}$ ?

Possible Answers:

$\frac{-x+5}{2x+3}$ $\displaystyle \frac{-x+5}{2x+3}$

$\frac{\left -(x-5 \right )}{2x+3}$ $\displaystyle \frac{\left -(x-5 \right )}{2x+3}$

$\frac{x-5}{\left -(2x+3 \right )}$ $\displaystyle \frac{x-5}{\left -(2x+3 \right )}$

$\frac{x+5}{2x + 3}$ $\displaystyle \frac{x+5}{2x + 3}$

$\frac{x-5}{-2x-3}$ $\displaystyle \frac{x-5}{-2x-3}$

Correct answer:

$\frac{x+5}{2x + 3}$ $\displaystyle \frac{x+5}{2x + 3}$

Explanation:

We know that $-\frac{a}{b}$ $\displaystyle -\frac{a}{b}$ is equivalent to $\frac{-a}{b}$ $\displaystyle \frac{-a}{b}$ or $\frac{a}{-b}$ $\displaystyle \frac{a}{-b}$.

By this property, there is no way to get $\frac{x+5}{2x+3}$ $\displaystyle \frac{x+5}{2x+3}$ from $-\frac{x-5}{2x+3}$ $\displaystyle -\frac{x-5}{2x+3}$.

Therefore the correct answer is $\frac{x+5}{2x+3}$ $\displaystyle \frac{x+5}{2x+3}$.

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #32 : Binomials

Example Question #301 : Variables

Example Question #302 : Variables

Example Question #303 : Variables

Example Question #304 : Variables

Example Question #305 : Variables

Example Question #306 : Variables

Example Question #4 : Solving Rational Expressions

Example Question #1 : Factoring Rational Expressions

Example Question #307 : Variables

All Algebra 1 Resources

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