Consider the following inequality:2(−3x+2)≤−2x−42(−3𝑥+2)≤−2𝑥−4Step 1 of 2 : Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.AnswerKeypadKeyboard ShortcutsIf all real numbers satisfy the inequality, select All Real Numbers. If no real number satisfies the inequality, select No Solution.Selecting one of the alternative options will replace the entered value(s) with the selected value. Otherwise, the entered answer is used.
Question
Consider the following inequality:2(−3x+2)≤−2x−42(−3𝑥+2)≤−2𝑥−4Step 1 of 2 : Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.AnswerKeypadKeyboard ShortcutsIf all real numbers satisfy the inequality, select All Real Numbers. If no real number satisfies the inequality, select No Solution.Selecting one of the alternative options will replace the entered value(s) with the selected value. Otherwise, the entered answer is used.
Solution
Let's solve the inequality step by step:
Given inequality: 2(-3x + 2) ≤ -2x - 4
Step 1: Distribute the 2 on the left side of the inequality:
-6x + 4 ≤ -2x - 4
Step 2: Add 6x to both sides of the inequality to isolate the variable term on one side:
4 ≤ 4x - 4
Step 3: Add 4 to both sides of the inequality to isolate the variable term:
8 ≤ 4x
Step 4: Divide both sides of the inequality by 4 to solve for x:
x ≥ 2
So, the solution to the inequality is x ≥ 2.
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