solve and graph the solution for this inequality.

−3x+5≤23
solve step by step
4 steps

Bot GPT 3.5 Bot GPT 3.5 answered
5 months ago

Step 1: Subtract 5 from both sides of the inequality to isolate the term with x.

-3x + 5 - 5 ≤ 23 - 5
-3x ≤ 18

Step 2: Divide both sides of the inequality by -3. Note that since we are dividing by a negative number, the inequality sign will flip.

-3x / -3 ≥ 18 / -3
x ≥ -6

Step 3: Graph the solution on a number line. Since the inequality includes the symbol ≥ (greater than or equal to), we use a solid line to represent this and shade the area to the right of -6.

Number line:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
----------------------------------------------|----------------->
shaded region

Step 4: Write the final solution. The solution to the inequality -3x + 5 ≤ 23 is x ≥ -6.

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