Question

Rearrange the first inequality to match the second inequality and fill in the blanks for the variables. Then select the appropriate intervals to create the solution set for this inequality. 4 x + 7 x + 1 < 11 x + 2

Answer 1

The inequality 4x + 7x + 1 < 11x + 2 simplifies to 1 < 2 after combining like terms and subtracting 11x from both sides. The resulting inequality is true for all x values, indicating that x can be any real number.

Step-by-step explanation:

Simplifying the Inequality

To rearrange the given inequality 4x + 7x + 1 < 11x + 2, we must first combine like terms and then isolate the variable on one side.

1. Combine like terms on the left side: 4x + 7x becomes 11x.
2. Subtract 11x from both sides to get all x terms on one side and the constants on the other: 11x + 1 - 11x < 11x + 2 - 11x, which simplifies to 1 < 2.
3. The inequality is now 1 < 2, which is true for all values of x. Thus, there is no need to find an interval for x since the inequality holds for any real number.

When simplifying algebraic expressions and inequalities, it's important to eliminate terms wherever possible to make the solution clearer and check if the solution is reasonable. Here, the simplified inequality is always true, indicating that x can be any real number.

Answer 2

The solution set would be all real numbers

Step-by-step explanation:

Remember that you should pass from one side to the other the terms which are similar, that is to say x with x and numbers with numbers. In doing so you must be sure to change the sign of the term if it is passed from one side to the other.

In this case it would be:

4x + 7x + 1 < 11x + 2

(Four plus seven is 11)

11x + 1 < 11x + 2

We can see that x is eliminated, because we change the sign on 11 to be -11:

11x - 11x + 1 < 2

1 < 2

This result means that no matter which value we give to x, the inequality will be always true. For that reason the answer is all real numbers