To solve the inequality \(-2x + 5 > -5\), we first isolate \(x\):
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Subtract 5 from both sides: \[ -2x > -5 - 5 \] \[ -2x > -10 \]
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Now, divide both sides by -2. Remember that when we divide or multiply by a negative number, we need to reverse the inequality sign: \[ x < 5 \]
The solution to the inequality is \(x < 5\), which indicates that \(x\) can take any value that is less than 5.
Now, we need to find the right representation on the number line options provided. The correct number line should show all the numbers to the left of 5 with an open circle at 5 since 5 is not included in the solution.
Among the options A, B, C, and D, the correct number line representation is one that has an arrow pointing left from 5 or shading to the left of 5.
Upon reviewing, option C and D are identical. If they show an open circle at 5 with shading to the left, then either one could represent the solution \(x < 5\).
However, I cannot visually see the number lines. Based on what to look for, choose the one that accurately shows \(x < 5\). If you have the visual for those options, choose the one marked correctly (open circle on 5 and shading or an arrow pointing left towards negative infinity).
If both C and D seem the same, select either one based on the proper representation.
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