Question: If 3(x + 2) < 2(x + 5), what is the value of x?
Options:
x < 1
x > 1
x = 1
x = 0
Correct Answer: x < 1
Solution:
Step 1: Distribute: 3x + 6 < 2x + 10. Step 2: Subtract 2x from both sides: x + 6 < 10. Step 3: Subtract 6: x < 4.
If 3(x + 2) < 2(x + 5), what is the value of x?
Practice Questions
Q1
If 3(x + 2) < 2(x + 5), what is the value of x?
x < 1
x > 1
x = 1
x = 0
Questions & Step-by-Step Solutions
If 3(x + 2) < 2(x + 5), what is the value of x?
Step 1: Distribute the numbers outside the parentheses. Multiply 3 by (x + 2) to get 3x + 6. Multiply 2 by (x + 5) to get 2x + 10. Now the inequality looks like this: 3x + 6 < 2x + 10.
Step 2: To get all the x terms on one side, subtract 2x from both sides of the inequality. This gives you: 3x - 2x + 6 < 10, which simplifies to x + 6 < 10.
Step 3: Now, to isolate x, subtract 6 from both sides. This results in: x < 10 - 6, which simplifies to x < 4.
Inequalities – Understanding how to manipulate and solve inequalities involving variables.
Distributive Property – Applying the distributive property to expand expressions.
Algebraic Manipulation – Performing operations such as addition and subtraction to isolate the variable.
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