Question

which values from the set {-2, 0, 1, 3, 5, 7} satisfy this inequality? -3x + 15 > 6 *solve or plug in to find out

Explanation:

Step1: Analyze the inequality

The inequality is \(-3x + 15>6\). First, solve for \(x\) algebraically. Subtract 15 from both sides: \(-3x>6 - 15\), so \(-3x>-9\). Then divide both sides by - 3 (remember to reverse the inequality sign when dividing by a negative number): \(x < 3\).

Step2: Check values from the set \(\{2,0,1,3,5,7\}\)

• For \(x = 2\): Substitute into \(-3x + 15\), we get \(-3(2)+15=-6 + 15 = 9\). Since \(9>6\), \(x = 2\) is a solution.
• For \(x = 0\): Substitute, \(-3(0)+15=0 + 15 = 15\). Since \(15>6\), \(x = 0\) is a solution.
• For \(x = 1\): Substitute, \(-3(1)+15=-3 + 15 = 12\). Since \(12>6\), \(x = 1\) is a solution.
• For \(x = 3\): Substitute, \(-3(3)+15=-9 + 15 = 6\). But \(6\) is not greater than \(6\), so \(x = 3\) is not a solution.
• For \(x = 5\): Substitute, \(-3(5)+15=-15 + 15 = 0\). Since \(0<6\), \(x = 5\) is not a solution.
• For \(x = 7\): Substitute, \(-3(7)+15=-21 + 15=-6\). Since \(-6<6\), \(x = 7\) is not a solution.

Answer:

The values from the set \(\{2,0,1,3,5,7\}\) that satisfy the inequality \(-3x + 15>6\) are \(2\), \(0\), and \(1\).