Solve and graph the solution for this inequality.
−3x+5≤23
Need Help? Solving and Graphing Two-Step Inequalities with Negative Coefficients
(16 points)
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To solve the inequality -3x + 5 ≤ 23, we need to isolate the variable x.
Step 1: Subtract 5 from both sides of the inequality:
-3x + 5 - 5 ≤ 23 - 5
-3x ≤ 18
Step 2: Divide both sides of the inequality by -3. Note that when you divide by a negative number, the direction of the inequality sign should be reversed:
-3x/(-3) ≥ 18/(-3)
x ≥ -6
Step 3: Graph the solution on a number line. We represent the solution by shading the region to the right of -6, including -6 itself.
Step 4: Draw an arrow to the right of -6 to indicate that all values greater than or equal to -6 satisfy the inequality.
Therefore, the solution to the inequality -3x + 5 ≤ 23 is x ≥ -6.
Graphically, it can be represented as a number line with a shaded region to the right of -6 and an arrow pointing to the right.