Algebra 1 : How to solve one-step equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #211 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{-41}=11\)

Possible Answers:

\(\displaystyle 451\)

\(\displaystyle -451\)

\(\displaystyle -241\)

\(\displaystyle 441\)

\(\displaystyle 241\)

Correct answer:

\(\displaystyle -451\)

Explanation:

In order to solve for \(\displaystyle x\), we need to isolate the variable on the left side of the equation. We will do this by performing the same operations to both sides of the equation.

\(\displaystyle \frac{x}{-41}=11\) 

Multiply both sides of the equation by \(\displaystyle -41\). When multiplying with one negative and one positive number, our answer is negative. 

\(\displaystyle (-41)\frac{x}{-41}=11(-41)\)

Solve.

\(\displaystyle x=-451\)

Example Question #212 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle \frac{x}{-1.3}=-1.5\)

Possible Answers:

\(\displaystyle -19.5\)

\(\displaystyle 19.5\)

\(\displaystyle 0.195\)

\(\displaystyle 1.95\)

\(\displaystyle -1.95\)

Correct answer:

\(\displaystyle 1.95\)

Explanation:

In order to solve for \(\displaystyle x\), we need to isolate the variable on the left side of the equation. We will do this by performing the same operations to both sides of the equation.

\(\displaystyle \frac{x}{-1.3}=-1.5\) 

Multiply both sides by \(\displaystyle -1.3\). When multiplying two negative numbers, our answer is positive. 

\(\displaystyle (-1.3)\frac{x}{-1.3}=-1.5(-1.3)\)

Solve.

\(\displaystyle x=1.95\)

Example Question #212 : Algebra 1

Solve for \(\displaystyle x\)\(\displaystyle 4x=9\).

Possible Answers:

\(\displaystyle \frac{1}{4}\)

\(\displaystyle \frac{9}{4}\)

\(\displaystyle -\frac{4}{9}\)

\(\displaystyle \frac{4}{9}\)

\(\displaystyle -\frac{9}{4}\)

Correct answer:

\(\displaystyle \frac{9}{4}\)

Explanation:

In order to solve for \(\displaystyle x\) in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to \(\displaystyle x\) that is the inverse (opposite) of what's currently being applied to \(\displaystyle x\).

Given \(\displaystyle 4x=9\), we see that \(\displaystyle x\) is being multiplied by \(\displaystyle 4\), so we need to divide both sides of the equation by \(\displaystyle 4\) to isolate it:

\(\displaystyle 4x=9\)

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

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

Example Question #214 : Algebra 1

Solve for \(\displaystyle x\)\(\displaystyle \frac{x}{8}=3\).

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 18\)

\(\displaystyle 22\)

\(\displaystyle 16\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 24\)

Explanation:

In order to solve for \(\displaystyle x\) in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to \(\displaystyle x\) that is the inverse (opposite) of what's currently being applied to \(\displaystyle x\).

Given \(\displaystyle \frac{x}{8}=3\), we see that \(\displaystyle x\) is being divided by \(\displaystyle 8\), so we need to multiply both sides of the equation by \(\displaystyle 8\) to isolate it:

\(\displaystyle \frac{x}{8}=3\)

\(\displaystyle (8)(\frac{x}{8})=3(8)\)

\(\displaystyle x=24\)

Example Question #215 : Algebra 1

Solve for \(\displaystyle x\)\(\displaystyle x+7=11\).

Possible Answers:

\(\displaystyle -4\)

\(\displaystyle 7\)

\(\displaystyle 11\)

\(\displaystyle 18\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 4\)

Explanation:

In order to solve for \(\displaystyle x\) in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to \(\displaystyle x\) that is the inverse (opposite) of what's currently being applied to \(\displaystyle x\).

Given \(\displaystyle x+7=11\), we see that \(\displaystyle 7\) is being added to \(\displaystyle x\), so we need to subtract both sides of the equation by \(\displaystyle 7\) to isolate \(\displaystyle x\):

\(\displaystyle x+7=11\)

\(\displaystyle x+7-7=11-7\)

\(\displaystyle x+7-7=11-7\)

\(\displaystyle x=4\)

Example Question #216 : Algebra 1

Solve for : \(\displaystyle x-5=4\).

Possible Answers:

\(\displaystyle -1\)

\(\displaystyle 1\)

\(\displaystyle -9\)

\(\displaystyle 5\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 9\)

Explanation:

In order to solve for in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to that is the inverse (opposite) of what's currently being applied to .

Given \(\displaystyle x-5=4\), we see that \(\displaystyle 5\) is being subtracted from , so we need to add \(\displaystyle 5\) to both sides of the equation to isolate \(\displaystyle x\):

\(\displaystyle x-5=4\)

\(\displaystyle x-5+5=4+5\)

\(\displaystyle x=9\)

Example Question #217 : Algebra 1

Solve for \(\displaystyle \frac{x}{6}=2\).

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle 12\)

\(\displaystyle -4\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 12\)

Explanation:

In order to solve for  in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to  that is the inverse (opposite) of what's currently being applied to .

Given \(\displaystyle \frac{x}{6}=2\), we see that  is being divided by \(\displaystyle 6\), so we need to multiply both sides of the equation by \(\displaystyle 6\) to isolate \(\displaystyle x\):

\(\displaystyle \frac{x}{6}=2\)

\(\displaystyle 6(\frac{x}{6})=(6)2\)

\(\displaystyle x=12\)

Example Question #218 : Algebra 1

Solve for \(\displaystyle 7x=2\).

Possible Answers:

\(\displaystyle -5\)

\(\displaystyle \frac{2}{7}\)

\(\displaystyle \frac{7}{2}\)

\(\displaystyle -\frac{7}{2}\)

\(\displaystyle -\frac{2}{7}\)

Correct answer:

\(\displaystyle \frac{2}{7}\)

Explanation:

In order to solve for  in the above equation, we must isolate it on one side of the equation. We can do this by applying an operation to  that is the inverse (opposite) of what's currently being applied to .

Given \(\displaystyle 7x=2\), we see that  is being multiplied by \(\displaystyle 7\), so we need to divide both sides of the equation by \(\displaystyle 7\) to isolate \(\displaystyle x\):

\(\displaystyle 7x=2\)

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

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

Example Question #219 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle 14+x=72\)

Possible Answers:

\(\displaystyle 29\)

\(\displaystyle 58\)

\(\displaystyle 86\)

\(\displaystyle 34\)

\(\displaystyle 66\)

Correct answer:

\(\displaystyle 58\)

Explanation:

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations on both sides of the given equation:

\(\displaystyle 14+x=72\) 

Subtract \(\displaystyle 14\) from both sides of the equation.

\(\displaystyle 14-14+x=72-14\)

Solve.

\(\displaystyle x=58\)

Example Question #220 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle -13+x=24\)

Possible Answers:

\(\displaystyle -37\)

\(\displaystyle 37\)

\(\displaystyle 35\)

\(\displaystyle 11\)

\(\displaystyle -11\)

Correct answer:

\(\displaystyle 37\)

Explanation:

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations on both sides of the given equation:

\(\displaystyle -13+x=24\) 

Add \(\displaystyle 13\) to both sides of the equation.

\(\displaystyle -13+13+x=24+13\)

Solve.

\(\displaystyle x=37\)

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