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Which value of x makes this inequality true? x+9<4x

A.4
B.1
C.3
D.2

User Jusx
by
7.6k points

1 Answer

3 votes

Answer:

A. 4

Explanation:

Given inequality:


x+9 < 4x

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:


\begin{aligned}x+9-x &amp; < 4x-x\\9&amp; < 3x\end{aligned}

Divide both sides of the inequality by 3:


\begin{aligned}(9)/(3)&amp; < (3x)/(3)\\\\3&amp; < x\\\\x&amp; > 3\end{aligned}

So the values of x that make the inequality true are:

  • Any value of x that is greater than 3.

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:


\begin{aligned}x+9&amp; < 4x\\x=4\implies 4+9&amp; < 4(4)\\13&amp; < 16\end{aligned}

As 13 is less than 16, the inequality is true when x = 4.

User Navnath
by
7.9k points

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