Question: Find the solution set for the inequality -2x + 3 > 1.
Options:
x < 1
x > 1
x < 2
x > 2
Correct Answer: x > 1
Solution:
Subtract 3 from both sides: -2x > -2. Then divide by -2 (reverse the inequality): x < 1.
Find the solution set for the inequality -2x + 3 > 1.
Practice Questions
Q1
Find the solution set for the inequality -2x + 3 > 1.
x < 1
x > 1
x < 2
x > 2
Questions & Step-by-Step Solutions
Find the solution set for the inequality -2x + 3 > 1.
Correct Answer: x < 1
Step 1: Start with the inequality -2x + 3 > 1.
Step 2: Subtract 3 from both sides to isolate the term with x. This gives you -2x > 1 - 3.
Step 3: Simplify the right side: -2x > -2.
Step 4: Now, divide both sides by -2. Remember, when you divide by a negative number, you must reverse the inequality sign. So, it becomes x < 1.
Step 5: The solution set is all values of x that are less than 1.
Inequalities – Understanding how to manipulate and solve inequalities, including the rule of reversing the inequality sign when dividing by a negative number.
Algebraic Manipulation – Skills in performing operations such as addition, subtraction, multiplication, and division on both sides of an inequality.
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