The solution to the inequality [tex]2(4 + 2x) \geq 5x + 5[/tex] will be [tex]x \leq 3[/tex] .
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
We have,
[tex]2(4 + 2x) \geq 5x + 5[/tex]
Now,
Simplify for [tex]2(4 + 2x)[/tex] ;
[tex]2(4 + 2x)[/tex]
[tex]8 + 4x[/tex]
Now,
So rewrite [tex]2(4 + 2x) \geq 5x + 5[/tex] ;
[tex](8 + 4x) \geq 5x + 5[/tex]
Now using distributive property ;
[tex](8 + 4x) \geq 5x + 5[/tex]
Move all terms containing [tex]x[/tex] to the left side,
[tex](8 + 4x- 5x ) \geq + 5[/tex]
[tex](8 -x ) \geq + 5[/tex]
[tex]( -x ) \geq + 5-8[/tex]
[tex]-x \geq -3[/tex]
⇒ [tex]x \leq 3[/tex]
Hence, we can say that the solution to the inequality [tex]2(4 + 2x) \geq 5x + 5[/tex] will be [tex]x \leq 3[/tex] .
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