Algebra 1 : How to solve two-step equations

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #61 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

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

Possible Answers:

\(\displaystyle 20\)

\(\displaystyle 10\)

\(\displaystyle 6\)

\(\displaystyle 12\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 10\)

Explanation:

\(\displaystyle 4+\frac{x}{2}=9\) Subtract \(\displaystyle 4\) to both sides. 

\(\displaystyle \frac{x}{2}=5\) Cross-multiply. 

\(\displaystyle x=10\)

Example Question #62 : How To Solve Two Step Equations

Solve for \(\displaystyle x.\)

\(\displaystyle 4x-6=-10\)

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle -1\)

\(\displaystyle 6\)

\(\displaystyle -10\)

\(\displaystyle -4\)

Correct answer:

\(\displaystyle -1\)

Explanation:

\(\displaystyle 4x-6=-10\) Isolate \(\displaystyle 4x\) by adding both sides by \(\displaystyle 6\).

\(\displaystyle 4x=-4\) Divide both sides by \(\displaystyle 4\) to just get \(\displaystyle x\).

\(\displaystyle x=-1\)

Example Question #61 : How To Solve Two Step Equations

Solve the following equation for \(\displaystyle x\).

\(\displaystyle 3x+11=23\)

Possible Answers:

\(\displaystyle x=4\)

\(\displaystyle x=24\)

\(\displaystyle x=-4\)

\(\displaystyle x=1\)

Correct answer:

\(\displaystyle x=4\)

Explanation:

\(\displaystyle 3x+11=23\)

Subtract 11 from both sides.

\(\displaystyle 3x=12\)

Divide each side by 3. 

\(\displaystyle x=4\)

Example Question #64 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 3x-7=14\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 63\)

\(\displaystyle -14\)

\(\displaystyle 21\)

\(\displaystyle -7\)

Correct answer:

\(\displaystyle 7\)

Explanation:

\(\displaystyle 3x-7=14\) 

Add \(\displaystyle 7\) to both sides.

\(\displaystyle 3x=21\) 

Divide both sides by \(\displaystyle 3\).

\(\displaystyle x=7\)

Example Question #65 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 9x-22=68\)

Possible Answers:

\(\displaystyle 10\)

\(\displaystyle \frac{46}{9}\)

\(\displaystyle -90\)

\(\displaystyle 90\)

\(\displaystyle -10\)

Correct answer:

\(\displaystyle 10\)

Explanation:

\(\displaystyle 9x-22=68\) 

Add \(\displaystyle 22\) to both sides.

\(\displaystyle 9x=90\) 

Divide both sides by \(\displaystyle 9\).

\(\displaystyle x=10\)

Example Question #66 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 4=\frac{x}{5}+3\)

Possible Answers:

\(\displaystyle -35\)

\(\displaystyle -5\)

\(\displaystyle 6\)

\(\displaystyle 5\)

\(\displaystyle 35\)

Correct answer:

\(\displaystyle 5\)

Explanation:

\(\displaystyle 4=\frac{x}{5}+3\) 

Subtract \(\displaystyle 3\) from both sides. 

\(\displaystyle 1=\frac{x}{5}\) 

Multiply both sides by \(\displaystyle 5\).

\(\displaystyle x=5\)

Example Question #67 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 7=\frac{x+2}{5}\)

Possible Answers:

\(\displaystyle 39\)

\(\displaystyle 37\)

\(\displaystyle 35\)

\(\displaystyle 33\)

\(\displaystyle 31\)

Correct answer:

\(\displaystyle 33\)

Explanation:

\(\displaystyle 7=\frac{x+2}{5}\) 

Multiply both sides by \(\displaystyle 5\).

\(\displaystyle 35=x+2\) 

Subtract \(\displaystyle 2\) from both sides.

\(\displaystyle x=33\)

Example Question #68 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle -12=\frac{x-10}{6}\)

Possible Answers:

\(\displaystyle 82\)

\(\displaystyle -72\)

\(\displaystyle -82\)

\(\displaystyle 62\)

\(\displaystyle -62\)

Correct answer:

\(\displaystyle -62\)

Explanation:

\(\displaystyle -12=\frac{x-10}{6}\) 

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

\(\displaystyle 6(-12)=\left ( \frac{x-10}{6} \right )6\)

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

\(\displaystyle -72=x-10\) 

Add \(\displaystyle 10\) to both sides. When adding a positive number to a negative number, we must compare the values excluding the sign. Since \(\displaystyle 72\) is greater than \(\displaystyle 10\) and is negative, our answer will be negative. We will then treat the left side of the equation as a subtraction problem.

\(\displaystyle -(72-10)=x-10+10\)

\(\displaystyle x=-62\)

Example Question #69 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle -11=\frac{x+3}{-8}\)

Possible Answers:

\(\displaystyle -91\)

\(\displaystyle 88\)

\(\displaystyle 85\)

\(\displaystyle 91\)

\(\displaystyle -85\)

Correct answer:

\(\displaystyle 85\)

Explanation:

\(\displaystyle -11=\frac{x+3}{-8}\) 

Multiply both sides by \(\displaystyle -8\).  

\(\displaystyle (-11)(-8)=\left ( \frac{x+3}{-8}\right )(-8)\)

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

\(\displaystyle 88=x+3\) 

Subtract both sides by \(\displaystyle 3\)

\(\displaystyle x=85\)

Example Question #70 : How To Solve Two Step Equations

Solve for \(\displaystyle x\).

\(\displaystyle 4x+6=-2\)

Possible Answers:

\(\displaystyle -2\)

\(\displaystyle -1\)

\(\displaystyle 4\)

\(\displaystyle 2\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle -2\)

Explanation:

\(\displaystyle 4x+6=-2\) 

Subtract \(\displaystyle 6\) 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.

\(\displaystyle 4x+6-6=-(2+6)\)

\(\displaystyle 4x=-8\) 

Divide both sides by \(\displaystyle 4\)

\(\displaystyle \frac{4x}{4}=\frac{(-8)}{4}\)

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

\(\displaystyle x=-2\)

Learning Tools by Varsity Tutors