Question: Find the solution set for the inequality -4x + 1 < 3.
Options:
x < -0.5
x > -0.5
x < 0.5
x > 0.5
Correct Answer: x < -0.5
Solution:
-4x + 1 < 3 => -4x < 2 => x > -0.5.
Find the solution set for the inequality -4x + 1 < 3.
Practice Questions
Q1
Find the solution set for the inequality -4x + 1 < 3.
x < -0.5
x > -0.5
x < 0.5
x > 0.5
Questions & Step-by-Step Solutions
Find the solution set for the inequality -4x + 1 < 3.
Correct Answer: x > -0.5
Step 1: Start with the inequality -4x + 1 < 3.
Step 2: Subtract 1 from both sides to isolate the term with x. This gives you -4x < 3 - 1.
Step 3: Simplify the right side. Now you have -4x < 2.
Step 4: To solve for x, divide both sides by -4. Remember, when you divide by a negative number, you must flip the inequality sign. So it becomes x > 2 / -4.
Step 5: Simplify 2 / -4 to get x > -0.5.
Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Manipulation – Applying operations to isolate the variable correctly.
Direction of Inequality – Recognizing how the direction of the inequality changes when multiplying or dividing by a negative number.
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