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Which is a correct first step in solving [tex]5-2x \ \textless \ 8x-3[/tex]?

A. [tex]5 \ \textless \ 6x - 3[/tex]

B. [tex]3x \ \textless \ 8x - 3[/tex]

C. [tex]5 \ \textless \ 10x - 3[/tex]

D. [tex]2 - 2x \ \textless \ 8x[/tex]

Sagot :

GinnyAnsweridn
Let's solve the inequality step by step:

The given inequality is:
[tex]\[ 5 - 2x < 8x - 3 \][/tex]

A common first step in solving inequalities is to get all terms involving the variable [tex]\( x \)[/tex] on one side and the constant terms on the other side. This helps in isolating the variable, making it easier to solve.

1. We should move the term [tex]\(-2x\)[/tex] to the right side. To do this, add [tex]\( 2x \)[/tex] to both sides:
[tex]\[ 5 - 2x + 2x < 8x - 3 + 2x \][/tex]
[tex]\[ 5 < 10x - 3 \][/tex]

So the inequality simplifies to:
[tex]\[ 5 < 10x - 3 \][/tex]

Hence, the correct first step is transforming the inequality to:
[tex]\[ 5 < 10x - 3 \][/tex]

Thus, the correct choice is:
[tex]\[ 5 < 10x - 3 \][/tex]
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