Question: Determine the solution for the inequality 7 - 3x < 1.
Options:
x < 2
x > 2
x ≤ 2
x ≥ 2
Correct Answer: x < 2
Solution:
7 - 3x < 1 => -3x < -6 => x > 2.
Determine the solution for the inequality 7 - 3x < 1.
Practice Questions
Q1
Determine the solution for the inequality 7 - 3x < 1.
x < 2
x > 2
x ≤ 2
x ≥ 2
Questions & Step-by-Step Solutions
Determine the solution for the inequality 7 - 3x < 1.
Correct Answer: x > 2
Step 1: Start with the inequality: 7 - 3x < 1.
Step 2: To isolate the term with x, subtract 7 from both sides: 7 - 3x - 7 < 1 - 7.
Step 3: This simplifies to: -3x < -6.
Step 4: Now, divide both sides by -3. Remember, when you divide by a negative number, you must flip the inequality sign: -3x / -3 > -6 / -3.
Step 5: This simplifies to: x > 2.
Inequalities – Understanding how to manipulate and solve inequalities, including reversing the inequality sign when multiplying or dividing by a negative number.
Algebraic Manipulation – Skills in rearranging equations and isolating variables to find solutions.
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