High School Math : How to solve one-step equations with integers in pre-algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #291 : High School Math

Solve for  if

 \(\displaystyle \frac{x}{5}=12\)

Possible Answers:

\(\displaystyle x=60\)

\(\displaystyle x=55\)

\(\displaystyle x=\frac{12}{5}\)

\(\displaystyle x=72\)

Correct answer:

\(\displaystyle x=60\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where  is being divided by a number, we must multiply both sides of the equation by the number.

In this case the number is \(\displaystyle 5\) so we multiply each side of the equation by \(\displaystyle 5\) to make it look like this

 \(\displaystyle 5(\frac{x}{5})=(12)5\)

The \(\displaystyle 5\)'s on the left side cancel so we only have .

Then we perform the necessary multiplication to get the answer of \(\displaystyle x=60\).

Example Question #292 : High School Math

Solve for \(\displaystyle x\) if \(\displaystyle \frac{x}{17}=4\)

Possible Answers:

\(\displaystyle x=\frac{4}{17}\)

\(\displaystyle x=66\)

\(\displaystyle x=68\)

\(\displaystyle x=72\)

Correct answer:

\(\displaystyle x=68\)

Explanation:

To solve for \(\displaystyle x\) we must get all of the numbers on the other side of the equation of \(\displaystyle x\).

To do this in a problem where \(\displaystyle x\) is being divided by a number, we must multiply both sides of the equation by the number.

In this case the number is \(\displaystyle 17\) so we multiply each side of the equation by \(\displaystyle 17\) to make it look like this \(\displaystyle 17(\frac{x}{17})=4(17)\)

The \(\displaystyle 17\)'s on the left side cancel so we only have .

Then we perform the necessary multiplication to get the answer of \(\displaystyle x=68\)

Example Question #293 : High School Math

Solve for  if \(\displaystyle x+32=44\)

Possible Answers:

\(\displaystyle x=12\)

\(\displaystyle x=14\)

\(\displaystyle x=8\)

\(\displaystyle x=76\)

Correct answer:

\(\displaystyle x=12\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is \(\displaystyle 32\) so we subtract \(\displaystyle 32\) from each side of the equation to make it look like this \(\displaystyle x+32-32=44-32\)

The \(\displaystyle 32\)'s on the left side cancel to get \(\displaystyle x=44-32\)

Then we perform the necessary subtraction to get the answer of  \(\displaystyle x=12\).

Example Question #294 : High School Math

Solve for  if \(\displaystyle 5x=80\)

Possible Answers:

\(\displaystyle x=85\)

\(\displaystyle x=400\)

\(\displaystyle x=16\)

\(\displaystyle x=75\)

Correct answer:

\(\displaystyle x=16\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where  is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is \(\displaystyle 5\) so we divide each side of the equation by \(\displaystyle 5\) to make it look like this \(\displaystyle \frac{5x}{5}=\frac{80}{5}\)

The \(\displaystyle 5\)'s cancel to leave  by itself.

Then we perform the necessary division to get the answer of \(\displaystyle x=16\).

Example Question #291 : High School Math

Solve for \(\displaystyle \small x\).

\(\displaystyle 14x-4=3\)

Possible Answers:

\(\displaystyle x=\frac{3}{10}\)

\(\displaystyle x=2\)

\(\displaystyle x=7\)

\(\displaystyle x=\frac{10}{3}\)

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

Correct answer:

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

Explanation:

To solve, you want to isolate the \(\displaystyle \small x\) on one side.

\(\displaystyle 14x-4=3\)

To get ride of the \(\displaystyle -4\), you add \(\displaystyle 4\) to both sides.

\(\displaystyle 14x-4+4=3+4\)

\(\displaystyle 14x=7\)

Then you divide by \(\displaystyle 14\) on both sides.

\(\displaystyle \frac{14x}{14}=\frac{7}{14}\)

 \(\displaystyle x = \frac{7}{14}=\frac{1}{2}\)

Example Question #296 : High School Math

Solve for  if \(\displaystyle x+15=72\).

Possible Answers:

\(\displaystyle x=72\)

\(\displaystyle x=67\)

\(\displaystyle x=57\)

\(\displaystyle x=60\)

Correct answer:

\(\displaystyle x=57\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is \(\displaystyle 15\) so we subtract \(\displaystyle 15\) from each side of the equation to make it look like this \(\displaystyle x+15-15=72-15\)

The \(\displaystyle 15\)'s on the left side cancel to get \(\displaystyle x=72-15\)

Then we perform the necessary subtraction to get the answer of  \(\displaystyle x=57\).

Example Question #11 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  if

 \(\displaystyle \frac{x}{16}=3\)

Possible Answers:

\(\displaystyle x=\frac{16}{3}\)

\(\displaystyle x=52\)

\(\displaystyle x=13\)

\(\displaystyle x=48\)

Correct answer:

\(\displaystyle x=48\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where  is being divided by a number, we must multiply both sides of the equation by the number.

In this case the number is \(\displaystyle 16\) so we multiply each side of the equation by \(\displaystyle 16\) to make it look like this

 \(\displaystyle (16)\frac{x}{16}=3(16)\)

The \(\displaystyle 16\)'s on the left side cancel so we only have .

Then we perform the necessary multiplication to get the answer of \(\displaystyle x=48\).

Example Question #12 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for \(\displaystyle x\) if 

\(\displaystyle x+44=1244\)

Possible Answers:

\(\displaystyle x=1244\)

\(\displaystyle x=1200\)

\(\displaystyle x=1288\)

\(\displaystyle x=1277\)

Correct answer:

\(\displaystyle x=1200\)

Explanation:

To solve for  we must get all of the numbers on the other side of the equation as .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is \(\displaystyle 44\) so we subtract \(\displaystyle 44\) from each side of the equation to make it look like this \(\displaystyle x+44-44=1244-44\)

The \(\displaystyle 44\)s on the left side cancel to get \(\displaystyle x=1244-44\)

Then we perform the necessary subtraction to get the answer of  \(\displaystyle x=1200\).

Example Question #13 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for the value of \(\displaystyle \small p\).

\(\displaystyle p+2=9\)

Possible Answers:

\(\displaystyle p=\frac{9}{2}\)

\(\displaystyle p=7\)

\(\displaystyle p=\frac{2}{9}\)

\(\displaystyle p=11\)

Correct answer:

\(\displaystyle p=7\)

Explanation:

\(\displaystyle p+2=9\)

We need to isolate the variable. Subtract \(\displaystyle \small 2\) from both sides

\(\displaystyle p+2-2=9-2\)

\(\displaystyle p=7\)

Example Question #14 : How To Solve One Step Equations With Integers In Pre Algebra

\(\displaystyle 4+x=32\)

Solve for \(\displaystyle x\).

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle 28\)

\(\displaystyle 8\)

\(\displaystyle 72\)

\(\displaystyle -12\)

Correct answer:

\(\displaystyle 28\)

Explanation:

\(\displaystyle 4+x=32\)

Subtract \(\displaystyle 4\) from both sides.

\(\displaystyle (4+x)-4=(32)-4\)

\(\displaystyle x=32-4\)

\(\displaystyle x=28\)

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