ACT Math : How to find out when an equation has no solution

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find Out When An Equation Has No Solution

Solve: 

\(\displaystyle -3(2x - 5) = 9 - 6x\)

Possible Answers:

\(\displaystyle \frac{15}{9}\)

No Solution 

\(\displaystyle 15\)

Infinitely Many Solutions 

\(\displaystyle 9\)

Correct answer:

No Solution 

Explanation:

First, distribute the \(\displaystyle -3\) to the terms inside the parentheses.

\(\displaystyle -3(2x - 5) = 9 - 6x\)

\(\displaystyle -6x + 15 = 9 - 6x\)

Add 6x to both sides. 

\(\displaystyle 15 = 9\)

This is false for any value of \(\displaystyle x\). Thus, there is no solution. 

Example Question #1 : Linear / Rational / Variable Equations

Solve \(\displaystyle \left | 3-4x\right |< 0\).

Possible Answers:

No solutions

\(\displaystyle x< \frac{3}{4}\)

\(\displaystyle x< \frac{4}{3}\)

\(\displaystyle x>\frac{3}{4}\)

\(\displaystyle x>\frac{4}{3}\)

Correct answer:

No solutions

Explanation:

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

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