To determine the solution set for the inequality \(-2x + 5 + x \leq 3x + 13\), we'll first simplify the inequality step by step.
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Combine like terms on the left side: \[ -2x + x + 5 \leq 3x + 13 \] This simplifies to: \[ -x + 5 \leq 3x + 13 \]
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Next, let's move all terms involving \(x\) to one side and constants to the other. Add \(x\) to both sides: \[ 5 \leq 3x + x + 13 \] \[ 5 \leq 4x + 13 \]
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Now, subtract \(13\) from both sides: \[ 5 - 13 \leq 4x \] \[ -8 \leq 4x \]
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Finally, divide both sides by \(4\): \[ -2 \leq x \]
Or, writing it in standard form: \[ x \geq -2 \]
This means the solution set is all values of \(x\) that are greater than or equal to \(-2\).
On a graph, this would typically be represented as a closed circle at \(-2\) (to indicate that \(-2\) is included in the solution) and a shading that extends to the right (to indicate all values greater than \(-2\)).
If you have specific graphs to choose from, look for the one that features a closed dot at \(-2\) and shading extending towards the right (i.e., toward positive infinity).
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