Questions: 2-3(x-1) ≥ 1x-7

Solution Steps

To solve the inequality \(2 - 3(x - 1) \geq x - 7\), we need to first simplify the expression by distributing and combining like terms. Then, isolate the variable \(x\) on one side of the inequality to find the solution set.

Start with the inequality: \[ 2 - 3(x - 1) \geq x - 7 \]

Distribute the \(-3\) across the terms inside the parentheses: \[ 2 - 3x + 3 \geq x - 7 \]

Combine like terms: \[ 5 - 3x \geq x - 7 \]

Add \(3x\) to both sides to get all terms involving \(x\) on one side: \[ 5 \geq 4x - 7 \]

Add \(7\) to both sides to isolate the term with \(x\): \[ 12 \geq 4x \]

Divide both sides by \(4\) to solve for \(x\): \[ 3 \geq x \]

This can be rewritten as: \[ x \leq 3 \]

Final Answer