The solution to the inequality \(2(4 + 2x) \geq 5x + 5\) will be \(x \leq 3\) .
What are inequalities ?
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,
\(2(4 + 2x) \geq 5x + 5\)
Now,
Simplify for \(2(4 + 2x)\) ;
\(2(4 + 2x)\)
\(8 + 4x\)
Now,
So rewrite \(2(4 + 2x) \geq 5x + 5\) ;
\((8 + 4x) \geq 5x + 5\)
Now using distributive property ;
\((8 + 4x) \geq 5x + 5\)
Move all terms containing \(x\) to the left side,
\((8 + 4x- 5x ) \geq + 5\)
\((8 -x ) \geq + 5\)
\(( -x ) \geq + 5-8\)
\(-x \geq -3\)
⇒ \(x \leq 3\)
Hence, we can say that the solution to the inequality \(2(4 + 2x) \geq 5x + 5\) will be \(x \leq 3\) .
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