Algebra 1 : How to solve one-step equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #31 : How To Solve One Step Equations

Solve for \(\displaystyle z\).

\(\displaystyle z-0=-9\)

Possible Answers:

\(\displaystyle -9\)

\(\displaystyle 9\)

\(\displaystyle 3\)

\(\displaystyle 1\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle -9\)

Explanation:

To isolate \(\displaystyle z\), we know anything added or subtracted by \(\displaystyle 0\) is the same.

This is the case. Answer is \(\displaystyle z=-9\)

Example Question #32 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle -7+x=9\)

Possible Answers:

\(\displaystyle -16\)

\(\displaystyle 63\)

\(\displaystyle 2\)

\(\displaystyle -2\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 16\)

Explanation:

To isolate \(\displaystyle x\), we would add \(\displaystyle 7\) on both sides.

The left side is just \(\displaystyle x.\) 

The right side, we will have 

\(\displaystyle x=9+7=16\).

\(\displaystyle x=16\)

Example Question #31 : Linear Equations

Solve the equation for \(\displaystyle x\)

\(\displaystyle x+14=6\)

Possible Answers:

\(\displaystyle x=-8\)

\(\displaystyle x=20\)

\(\displaystyle x=8\)

\(\displaystyle x=14\)

Correct answer:

\(\displaystyle x=-8\)

Explanation:

\(\displaystyle x+14=6\)

Isolate \(\displaystyle x\) by subtracting 14 from each side of the equation.

6 minus 14 is negative 8, so \(\displaystyle x=8\).

Example Question #32 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle 14x-45=53\)

Possible Answers:

\(\displaystyle \frac{-4}{7}\)

\(\displaystyle \frac{4}{7}\)

\(\displaystyle 7\)

\(\displaystyle 6\)

\(\displaystyle -7\)

Correct answer:

\(\displaystyle 7\)

Explanation:

\(\displaystyle 14x-45=53\) 

Add \(\displaystyle 45\) to both sides.

\(\displaystyle 14x=98\) 

Divide both sides by \(\displaystyle 14\).

\(\displaystyle x=7\)

Example Question #33 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle 6x+5=-31\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle -6\)

\(\displaystyle \frac{13}{3}\)

\(\displaystyle \frac{-13}{3}\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle -6\)

Explanation:

\(\displaystyle 6x+5=-31\) 

Subtract \(\displaystyle 5\) from both sides. Since we are essentially adding two negative numbers, we will treat the right side of the equation as an addition problem and put a negative sign afterwards.

\(\displaystyle 6x+5-5=-(31+5)\)

\(\displaystyle 6x=-36\) 

Divide both sides by \(\displaystyle 6\).

\(\displaystyle \frac{6x}{6}=\frac{(-36)}{6}\)

When we divide a negative number by a positive number the answer is always negative.

\(\displaystyle x=-6\)

Example Question #32 : How To Solve One Step Equations

Solve for \(\displaystyle x\)

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

Possible Answers:

\(\displaystyle -23\)

\(\displaystyle 41\)

\(\displaystyle 18\)

\(\displaystyle 23\)

\(\displaystyle -41\)

Correct answer:

\(\displaystyle 41\)

Explanation:

\(\displaystyle x+(-32)=9\) 

Adding a negative number is the same operation as subtracting a positive number. Thus, the left side of the equation can be written as follows:

\(\displaystyle x-32=9\)

Add \(\displaystyle 32\) to both sides.

\(\displaystyle x=41\)

Example Question #33 : How To Solve One Step Equations

Solve for \(\displaystyle x.\)

\(\displaystyle x+(-43)=-21\)

Possible Answers:

\(\displaystyle 64\)

\(\displaystyle -64\)

\(\displaystyle -22\)

\(\displaystyle 22\)

\(\displaystyle 26\)

Correct answer:

\(\displaystyle 22\)

Explanation:

\(\displaystyle x+(-43)=-21\) 

Adding a negative number is the same operation as subtracting a positive number. Thus, the left side of the equation can be written as follows:

\(\displaystyle x-43=-21\)

Add \(\displaystyle 43\) to both sides. 

\(\displaystyle x-43+43=-21+43\)

Since \(\displaystyle 43\) is greater than \(\displaystyle 21\) and is positive, our answer will be positive. We will rewrite the right side of the equation and treat it as a subtraction problem.

\(\displaystyle x=43-21\)

\(\displaystyle x=22\)

Example Question #33 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle x-9=3\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 14\)

\(\displaystyle 12\)

\(\displaystyle -12\)

\(\displaystyle -6\)

Correct answer:

\(\displaystyle 12\)

Explanation:

\(\displaystyle x-9=3\) 

Add \(\displaystyle 9\) to both sides.

\(\displaystyle x=12\)

Example Question #36 : Algebra 1

Solve for \(\displaystyle x\).

\(\displaystyle x-(-17)=21\)

Possible Answers:

\(\displaystyle 38\)

\(\displaystyle 16\)

\(\displaystyle -4\)

\(\displaystyle -38\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 4\)

Explanation:

\(\displaystyle x-(-17)=21\) 

Subtracting a negative number is the same operation as adding a positive number. Thus, the left side of the equation can be written as follows:

\(\displaystyle x+17=21\)

Subtract \(\displaystyle 17\) from both sides.

\(\displaystyle x=4\)

Example Question #34 : Linear Equations

Solve for \(\displaystyle x\).

\(\displaystyle x+19=34\)

Possible Answers:

\(\displaystyle 18\)

\(\displaystyle 51\)

\(\displaystyle 17\)

\(\displaystyle 53\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle 15\)

Explanation:

\(\displaystyle x+19=34\) 

Subtract \(\displaystyle 19\) from both sides.

\(\displaystyle x=15\)

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