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Choose the missing step in the given solution to the inequality [tex]-2x - 14 \ \textgreater \ -4 + 3x[/tex].

[tex]\[
\begin{array}{r}
-2x - 14 \ \textgreater \ -4 + 3x \\
-5x - 14 \ \textgreater \ -4 \\
x \ \textless \ -2
\end{array}
\][/tex]

A. \(-5x < 10\)

B. \(-5x > -18\)

C. \(-5x > 18\)

D. [tex]\(-5x \ \textgreater \ 10\)[/tex]

Sagot :

GinnyAnsweridn
Sure, let's go through the inequality step by step and find the missing step.

Given the inequality:
[tex]\[ -2x - 14 > -4 + 3x \][/tex]

Step 1: Move all terms involving \( x \) to one side of the inequality.
[tex]\[ -2x - 3x - 14 > -4 \][/tex]
Thus, combining like terms:
[tex]\[ -5x - 14 > -4 \][/tex]

Step 2: Isolate \( x \) by adding 14 to both sides of the inequality.
[tex]\[ -5x - 14 + 14 > -4 + 14 \][/tex]
[tex]\[ -5x > 10 \][/tex]

Step 3: Divide both sides by -5. Remember, when you divide by a negative number, you need to reverse the inequality sign.
[tex]\[ x < -2 \][/tex]

So, the missing step in the given solution is:
[tex]\[ -5x > 10 \][/tex]

Therefore, the correct answer is:
[tex]\[ -5x > 10 \][/tex]
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