TACHS Math : Inequalities

Study concepts, example questions & explanations for TACHS Math

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Example Questions

Example Question #1 : Algebra

Solve the following inequality:

\(\displaystyle 10x+44>84\)

Possible Answers:

\(\displaystyle x< 128\)

\(\displaystyle x< 4\)

\(\displaystyle x>40\)

\(\displaystyle x>4\)

\(\displaystyle x< 40\)

Correct answer:

\(\displaystyle x>4\)

Explanation:

In algebra an inequality is a relationship that holds through different values of a variable. An inequality is considered to be solved when the variable is isolated to one side of the inequality. We will do this by performing the reverse of the operations that were done to the variable. It is important to note that what is done to one side of the inequality needs to be done on the other. 

Let's start by writing the inequality. 

\(\displaystyle 10x+44>84\) 

Subtract \(\displaystyle 44\) from both sides of the inequality. 

\(\displaystyle 10x+44-44>84-44\)

\(\displaystyle 10x>40\)

Divide each side of the inequality by \(\displaystyle 10\).

\(\displaystyle \frac{10x}{10}>\frac{40}{10}\)

Solve.

\(\displaystyle x>4\)

The variable is greater than four.

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