2z−4≤−3z+62𝑧−4≤−3𝑧+6Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.Answer2 PointsKeypadKeyboard 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
2z−4≤−3z+62𝑧−4≤−3𝑧+6Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.Answer2 PointsKeypadKeyboard 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
To solve the inequality 2z - 4 ≤ -3z + 6, follow these steps:
Step 1: Add 3z to both sides of the inequality to get 2z + 3z - 4 ≤ 6, which simplifies to 5z - 4 ≤ 6.
Step 2: Add 4 to both sides of the inequality to get 5z ≤ 10.
Step 3: Divide both sides of the inequality by 5 to solve for z. This gives you z ≤ 2.
So, the solution to the inequality is z ≤ 2.
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