High School Math : Algebraic Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #53 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for \(\displaystyle x\)

 

\(\displaystyle x - 3 = 12\)

Possible Answers:

\(\displaystyle x = 15\)

\(\displaystyle x = 36\)

There are infinite solutions

There is no solution

\(\displaystyle x = 9\)

Correct answer:

\(\displaystyle x = 15\)

Explanation:

When solving a one-step equation it is important to remember to isolate \(\displaystyle x\) by performing the inverse operations. Note that in our original equation, \(\displaystyle 3\) is being added to \(\displaystyle x\). Thus, we want to subtract \(\displaystyle 3\) from both sides to do the inverse operation. 

Then, \(\displaystyle x - 3 + 3 = 12 + 3\)

So, \(\displaystyle x = 15\)

 

Example Question #61 : How To Solve One Step Equations With Integers In Pre Algebra

\(\displaystyle x+15=6\)

Solve for \(\displaystyle x\).

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle -21\)

\(\displaystyle \frac{2}{5}\)

\(\displaystyle 21\)

\(\displaystyle -9\)

Correct answer:

\(\displaystyle -9\)

Explanation:

To solve \(\displaystyle x+15=6\), we need to subtract \(\displaystyle 15\) from both sides.

\(\displaystyle x+15-15=6-15\)

\(\displaystyle x=6-15\)

\(\displaystyle x=-9\)

Example Question #62 : How To Solve One Step Equations With Integers In Pre Algebra

\(\displaystyle x+5=34\)

Solve for \(\displaystyle x\).

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 170\)

\(\displaystyle \frac{34}{5}\)

\(\displaystyle 39\)

\(\displaystyle 29\)

Correct answer:

\(\displaystyle 29\)

Explanation:

To solve \(\displaystyle x+5=34\), subtract \(\displaystyle 5\) from both sides.

\(\displaystyle x+5-5=34-5\)

\(\displaystyle x=34-5\)

\(\displaystyle x=29\)

Example Question #63 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle x+9=32\)

Possible Answers:

\(\displaystyle x=39\)

\(\displaystyle x=23\)

\(\displaystyle x=21\)

\(\displaystyle x=41\)

Correct answer:

\(\displaystyle x=23\)

Explanation:

To solve for , subtract \(\displaystyle 9\) from both sides of the equation:

\(\displaystyle x+9-9=32-9\)

\(\displaystyle x=32-9\)

\(\displaystyle x=23\)

Example Question #64 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle \frac{x}{16}=4\)

Possible Answers:

\(\displaystyle x=4\)

\(\displaystyle x=8\)

\(\displaystyle x=64\)

\(\displaystyle x=48\)

Correct answer:

\(\displaystyle x=64\)

Explanation:

To solve for , multiply both sides of the equation by \(\displaystyle 16\):

\(\displaystyle \frac{x}{16}\cdot 16=4\cdot 16\)

\(\displaystyle x=4\cdot 16\)

\(\displaystyle x=64\)

Example Question #65 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle x-18=72\)

Possible Answers:

\(\displaystyle x=54\)

\(\displaystyle x=75\)

\(\displaystyle x=90\)

\(\displaystyle x=80\)

Correct answer:

\(\displaystyle x=90\)

Explanation:

To solve for , add \(\displaystyle 18\) to both sides of the equation:

\(\displaystyle x-18+18=72+18\)

\(\displaystyle x=72+18\)

\(\displaystyle x=90\)

Example Question #66 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle 12x=156\)

Possible Answers:

\(\displaystyle x=13\)

\(\displaystyle x=181\)

\(\displaystyle x=3124\)

\(\displaystyle x=81\)

Correct answer:

\(\displaystyle x=13\)

Explanation:

To solve for , divide each side of the equation by \(\displaystyle 12\):

\(\displaystyle \frac{12x}{12}=\frac{156}{12}\)

\(\displaystyle x=\frac{156}{12}\)

\(\displaystyle x=13\)

Example Question #66 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle 5x=90\)

Possible Answers:

\(\displaystyle x=18\)

\(\displaystyle x=80\)

\(\displaystyle x=15\)

\(\displaystyle x=35\)

Correct answer:

\(\displaystyle x=18\)

Explanation:

To solve for ,  divide both sides of the equation by \(\displaystyle 5\):

\(\displaystyle \frac{5x}{5}=\frac{90}{5}\)

\(\displaystyle x=18\)

Example Question #67 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for  when \(\displaystyle x-918=1332\)

Possible Answers:

\(\displaystyle x=289\)

\(\displaystyle x=2250\)

\(\displaystyle x=2575\)

\(\displaystyle x=1275\)

Correct answer:

\(\displaystyle x=2250\)

Explanation:

To solve for , add \(\displaystyle 918\) to both sides of the equation:

\(\displaystyle x-918+918=1332+918\)

\(\displaystyle x=2250\)

Example Question #201 : Pre Algebra

Solve for  when \(\displaystyle \frac{x}{7}=9\)

Possible Answers:

\(\displaystyle x=\frac{9}{7}\)

\(\displaystyle x=54\)

\(\displaystyle x=9\)

\(\displaystyle x=63\)

Correct answer:

\(\displaystyle x=63\)

Explanation:

To solve for , multiply both sides of the equation by \(\displaystyle 7\):

\(\displaystyle \frac{x}{7}\cdot 7=9\cdot 7\)

\(\displaystyle x=9\cdot 7\)

\(\displaystyle x=63\)

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