Praxis Math : How to reason and solve one-variable equations and inequalities

Study concepts, example questions & explanations for Praxis Math

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Example Questions

Example Question #1 : Algebra And Functions

Solve for \(\displaystyle x\).

\(\displaystyle 18+4x=98\)

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 20\)

\(\displaystyle 40\)

Cannot be determined

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 20\)

Explanation:

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

Let's begin by rewriting the given equation.

\(\displaystyle 18+4x=98\)

Subtract \(\displaystyle 18\) from both sides of the equation.

\(\displaystyle 18-18+4x=98-18\)

Simplify.

\(\displaystyle 4x=80\)

Divide both sides of the equation by \(\displaystyle 4\).

\(\displaystyle \frac{4x}{4}=\frac{80}{4}\)

Solve.

\(\displaystyle x=20\)

Example Question #1 : How To Reason And Solve One Variable Equations And Inequalities

Solve for \(\displaystyle x\).

\(\displaystyle 21+5x=71\)

Possible Answers:

Cannot be determined

\(\displaystyle 15\)

\(\displaystyle 25\)

\(\displaystyle 10\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 10\)

Explanation:

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

Let's begin by rewriting the given equation.

\(\displaystyle 21+5x=71\)

Subtract \(\displaystyle 21\) from both sides of the equation.

\(\displaystyle 21-21+5x=71-21\)

Simplify.

\(\displaystyle 5x=50\)

Divide both sides of the equation by \(\displaystyle 5\).

\(\displaystyle \frac{5x}{5}=\frac{50}{5}\)

Solve.

\(\displaystyle x=10\)

Example Question #2 : How To Reason And Solve One Variable Equations And Inequalities

Solve for \(\displaystyle x\).

\(\displaystyle 6x-22=44\)

Possible Answers:

\(\displaystyle 9\)

Cannot be determined

\(\displaystyle 13\)

\(\displaystyle 11\)

\(\displaystyle 21\)

Correct answer:

\(\displaystyle 11\)

Explanation:

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

Let's begin by rewriting the given equation.

\(\displaystyle 6x-22=44\)

Add \(\displaystyle 22\) to both sides of the equation.

\(\displaystyle 6x-22+22=44+22\)

Simplify.

\(\displaystyle 6x=66\)

Divide both sides of the equation by \(\displaystyle 6\).

\(\displaystyle \frac{6x}{6}=\frac{66}{6}\)

Solve.

\(\displaystyle x=11\)

Example Question #3 : How To Reason And Solve One Variable Equations And Inequalities

Solve for \(\displaystyle x\).

\(\displaystyle 9x-18=108\)

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 14\)

\(\displaystyle 4\)

\(\displaystyle 18\)

Cannot be determined 

Correct answer:

\(\displaystyle 14\)

Explanation:

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

Let's begin by rewriting the given equation.

\(\displaystyle 9x-18=108\)

Add \(\displaystyle 18\) to both sides of the equation.

\(\displaystyle 9x-18+18=108+18\)

Simplify.

\(\displaystyle 9x=126\)

Divide both sides of the equation by \(\displaystyle 9\).

\(\displaystyle \frac{9x}{9}=\frac{126}{9}\)

Solve.

\(\displaystyle x=14\)

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