Questions: Which represents the solution set to the inequality -1.5(4 x+1) ≥ 4.5-2.5(x+1) ? x ≥ -1 x ≥ 7/16 (-∞,-1] (-∞, 7/16]

Which represents the solution set to the inequality -1.5(4 x+1) ≥ 4.5-2.5(x+1) ? x ≥ -1 x ≥ 7/16 (-∞,-1] (-∞, 7/16]
Transcript text: Which represents the solution set to the inequality $-1.5(4 x+1) \geq 4.5-2.5(x+1)$ ? $x \geq-1$ $x \geq \frac{7}{16}$ $(-\infty,-1]$ $\left(-\infty, \frac{7}{16}\right]$
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Solution

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Solution Steps

Step 1: Expand both sides of the inequality

Expand the left side: \[ -1.5(4x + 1) = -6x - 1.5 \] Expand the right side: \[ 4.5 - 2.5(x + 1) = 4.5 - 2.5x - 2.5 = 2 - 2.5x \]

Step 2: Rewrite the inequality with expanded terms

The inequality becomes: \[ -6x - 1.5 \geq 2 - 2.5x \]

Step 3: Move all terms involving \( x \) to one side and constants to the other

Add \( 6x \) to both sides: \[ -1.5 \geq 2 + 3.5x \] Subtract \( 2 \) from both sides: \[ -3.5 \geq 3.5x \]

Step 4: Solve for \( x \)

Divide both sides by \( 3.5 \): \[ x \leq -1 \]

Final Answer

\(\boxed{x \leq -1}\)

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