Solve the inequality 14≤-14-512𝑥 and write the solution using:Inequality Notation: Graph the solution below:
Question
Solve the inequality 14≤-14-512𝑥 and write the solution using:Inequality Notation: Graph the solution below:
Solution
To solve the inequality 14 ≤ -14 - 512x, follow these steps:
Step 1: Add 14 to both sides to isolate the term with x: 14 + 14 ≤ -14 - 512x + 14 28 ≤ -512x
Step 2: Divide both sides by -512 to solve for x. Remember, when you divide or multiply an inequality by a negative number, the direction of the inequality sign changes: 28 / -512 ≥ x or x ≤ -28 / 512
Step 3: Simplify the fraction: x ≤ -0.0546875
So, the solution in inequality notation is x ≤ -0.0546875.
To graph this solution, you would draw a number line, put a solid dot on -0.0546875 (because the value is included in the solution), and draw a line extending to the left from this point (because x is less than or equal to -0.0546875).
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