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Solve this inequality

Solve this inequality-example-1
User ChuongPham
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\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }

Separate the inequality compound in the inequality system.


\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }

We solve to: 10 - 2x < 28

Order the unknown terms to the left side of the equation.
\boxed{\bf{-2x < 28-10 }}

Calculate the sum or difference.


\boxed{\bf{-2x < 18 }}

Divide both sides of the equation by the coefficient of the invariable.
\boxed{\bf{x > -(18)/(2) }}

Clear the common factor


\boxed{\bf{x > -9} }}

We solve to: 10 - 2x ≥ -8

Order the unknown terms to the left side of the equation.


\boxed{\bf{-2x\geq -8-10 }}

Calculate the sum or difference.


\boxed{\bf{-2x\geq -18 }}

Divide both sides of the equation by the coefficient of the invariable.


\boxed{\bf{x\leq (-18)/(-2) }}

Determine the sign of multiplication and division.


\boxed{\bf{x\leq (18)/(2) }}

Clear the common factor


\boxed{\bf{x\leq 9}}


\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }

We find the intersection.

Answer =
\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }

Alternative forms: x ∈ (-9, 9]

User Gabrielmaldi
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