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17. Solve the following inequality: [tex]-1 + 6(-1 - 3x) \ \textgreater \ -39 - 2x[/tex]

A. [tex]x \ \textless \ 3[/tex]
B. [tex]x \ \textless \ -10[/tex]
C. [tex]x \ \textless \ -3[/tex]
D. [tex]x \ \textless \ 2[/tex]

Sagot :

GinnyAnswer
Let's solve the inequality step by step.

First, we start with the given inequality:
[tex]\[ -1 + 6(-1 - 3x) > -39 - 2x \][/tex]

Step 1: Distribute the 6 across the terms inside the parentheses:
[tex]\[ -1 + 6(-1) + 6(-3x) > -39 - 2x \][/tex]
[tex]\[ -1 - 6 - 18x > -39 - 2x \][/tex]

Step 2: Combine like terms on the left side:
[tex]\[ -7 - 18x > -39 - 2x \][/tex]

Step 3: Add 18x to both sides to get all x terms on one side:
[tex]\[ -7 > -39 + 16x \][/tex]

Step 4: Add 39 to both sides to isolate the term involving x:
[tex]\[ 32 > 16x \][/tex]

Step 5: Divide both sides by 16 to solve for x:
[tex]\[ 2 > x \][/tex]
which can also be written as:
[tex]\[ x < 2 \][/tex]

Thus, the solution to the inequality is:
[tex]\[ x < 2 \][/tex]

The correct answer is:
D. [tex]\( x < 2 \)[/tex]
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