Algebra 1 : Proportions

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #31 : Proportions

Solve for \(\displaystyle x\).

\(\displaystyle \frac{1}{2}=\frac{4}{x}\)

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 8\)

\(\displaystyle 5\)

\(\displaystyle 3\)

\(\displaystyle \frac{1}{2}\)

Correct answer:

\(\displaystyle 8\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{1}{2}=\frac{4}{x}\)

We have \(\displaystyle 2*4=1*x\)

We get \(\displaystyle 8=x\)

Example Question #1161 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle \frac{1}{3}=\frac{5}{x}\)

Possible Answers:

\(\displaystyle 3\)

\(\displaystyle 15\)

\(\displaystyle 6\)

\(\displaystyle 8\)

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 15\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{1}{3}=\frac{5}{x}\)

We have \(\displaystyle 3*5=1*x\)

We get \(\displaystyle 15=x\)

Example Question #1162 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle \frac{5}{4}=\frac{25}{2x}\)

Possible Answers:

\(\displaystyle 25\)

\(\displaystyle 10\)

\(\displaystyle 5\)

\(\displaystyle 100\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 10\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{5}{4}=\frac{25}{2x}\)

We have \(\displaystyle 4*25=5*2x\).

We now have \(\displaystyle 100=10x\).

Divide both sides by \(\displaystyle 10\), we get \(\displaystyle 10=x\)

Example Question #1163 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle \frac{9}{4}=\frac{18}{2x}\)

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 72\)

\(\displaystyle 3\)

\(\displaystyle 24\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle 4\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{9}{4}=\frac{18}{2x}\)

We have \(\displaystyle 4*18=9*2x\).

We now have \(\displaystyle 72=18x\).

Divide both sides by \(\displaystyle 18\), we get \(\displaystyle 4=x\)

Example Question #1164 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle \frac{3}{7}=\frac{x}{2}\)

Possible Answers:

\(\displaystyle 67\)

\(\displaystyle \frac{5}{7}\)

\(\displaystyle \frac{6}{7}\)

\(\displaystyle \frac{8}{9}\)

\(\displaystyle \frac{7}{6}\)

Correct answer:

\(\displaystyle \frac{6}{7}\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{3}{7}=\frac{x}{2}\)

We have \(\displaystyle 3*2=7*x\).

We now have \(\displaystyle 6=7x\).

Divide both sides by \(\displaystyle 7\), we get \(\displaystyle \frac{6}{7}=x\)

Example Question #31 : Proportions

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{9}=\frac{4}{13}\)

Possible Answers:

\(\displaystyle \frac{13}{36}\)

\(\displaystyle 1\)

\(\displaystyle 13\)

\(\displaystyle \frac{36}{13}\)

\(\displaystyle \frac{24}{17}\)

Correct answer:

\(\displaystyle \frac{36}{13}\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{x}{9}=\frac{4}{13}\)

We have \(\displaystyle 4*9=13*x\).

We now have \(\displaystyle 36=13x\).

Divide both sides by \(\displaystyle 13\), we get \(\displaystyle \frac{36}{13}=x\)

Example Question #1166 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle \frac{6}{x}=\frac{x}{6}\)

Possible Answers:

\(\displaystyle \pm6\)

\(\displaystyle 6\)

\(\displaystyle 36\)

\(\displaystyle \pm36\)

\(\displaystyle -6\)

Correct answer:

\(\displaystyle \pm6\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{6}{x}=\frac{x}{6}\)

We have \(\displaystyle 6*6=x*x\).

We now have \(\displaystyle 36=x^2\)

Take square root on both sides. Remember, when we do that the answer is \(\displaystyle \pm \sqrt{36}\).

Two negative or two positive numbers multiplied can give us a positve value.  \(\displaystyle 6\) is the answer to that perfect square and we add the positive and negative sign to get \(\displaystyle \pm6\).

Example Question #1167 : Linear Equations

\(\displaystyle \frac{x}{-3}=\frac{27}{-x}\)

Possible Answers:

\(\displaystyle \pm81\)

\(\displaystyle 81\)

\(\displaystyle 9\)

\(\displaystyle -9\)

\(\displaystyle \pm9\)

Correct answer:

\(\displaystyle \pm9\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{x}{-3}=\frac{27}{-x}\)

We have \(\displaystyle -3*27=-x*x\).

When multiplying a negative and positive number, our answer is negative.

We now have \(\displaystyle -81=-x^2\).

We can divide both sides by \(\displaystyle -1\) to get \(\displaystyle 81=x^2\)

Take square root on both sides. Remember, when we do that the answer is \(\displaystyle \pm \sqrt{81}\). Two negative or two positive numbers multiplied can give us a positve value.  \(\displaystyle 9\) is the answer to that perfect square and we add the positive and negative sign to get \(\displaystyle \pm9\).

Example Question #31 : Proportions

Solve for \(\displaystyle x\).

\(\displaystyle \frac{1}{2}=\frac{5}{x+4}\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 10\)

\(\displaystyle 14\)

\(\displaystyle -6\)

\(\displaystyle -14\)

Correct answer:

\(\displaystyle 6\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{1}{2}=\frac{5}{x+4}\)

We have \(\displaystyle 2*5=1*(x+4)\).

Remember we treat the expression and place into a parantheses. We take care of the parantheses first and distribute the \(\displaystyle 1\).

We have \(\displaystyle 10=x+4\).

Subtract both sides by \(\displaystyle 4\)

We get \(\displaystyle 6=x\)

Example Question #32 : Proportions

Solve for \(\displaystyle x\).

\(\displaystyle \frac{6}{7}=\frac{12}{x-2}\)

Possible Answers:

\(\displaystyle 10\)

\(\displaystyle 20\)

\(\displaystyle 16\)

\(\displaystyle 14\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 16\)

Explanation:

To solve for \(\displaystyle x\), we just cross-multiply.

\(\displaystyle \frac{6}{7}=\frac{12}{x-2}\)

We have \(\displaystyle 7*12=6*(x-2)\).

Remember we treat the expression and place into a parantheses. We take care of the parantheses first and distribute the \(\displaystyle 6\).

We have \(\displaystyle 84=6x-12\).

Add both sides by \(\displaystyle 12\).

We have \(\displaystyle 6x=96\)

Then divide both sides by \(\displaystyle 6\)

We get \(\displaystyle 16=x\)

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