Question

what is the value of ( x ) in the inequality:
( 5x - 18 geq 2(4x - 15) )
( \bigcirc x leq -4 )
( \bigcirc x geq -4 )
( \bigcirc x leq 4 )
( \bigcirc x geq 4 )

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the inequality \(5x - 18\geq2(4x - 15)\). Using the distributive property \(a(b - c)=ab - ac\), here \(a = 2\), \(b = 4x\) and \(c = 15\), so \(2(4x-15)=2\times4x-2\times15 = 8x-30\). The inequality becomes \(5x - 18\geq8x - 30\).

Step2: Move the terms with x to one side

Subtract \(5x\) from both sides of the inequality: \(5x-18 - 5x\geq8x - 30-5x\). This simplifies to \(-18\geq3x - 30\).

Step3: Isolate the term with x

Add 30 to both sides of the inequality: \(-18 + 30\geq3x-30 + 30\). We get \(12\geq3x\).

Step4: Solve for x

Divide both sides of the inequality by 3: \(\frac{12}{3}\geq\frac{3x}{3}\). Which simplifies to \(4\geq x\), or \(x\leq4\).

Answer:

\(x\leq4\) (corresponding to the option " \(x\leq4\)")