Solve the inequality. Graph the solution set and write it in interval notation.

Question

1/3 * (x + 3) < 1/7 * (3x + 4)

Write the answer in interval notation.
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(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Answer 1

To solve the inequality 1/3 * (x + 3) < 1/7 * (3x + 4), we need to find the values of x that satisfy the inequality.

Let's begin by simplifying the inequality:

1/3 * (x + 3) < 1/7 * (3x + 4)

Multiplying both sides of the inequality by 21 (the least common denominator of 3 and 7) to eliminate fractions, we get:

7(x + 3) < 3(3x + 4)

Expanding both sides, we have:

7x + 21 < 9x + 12

Subtracting 9x from both sides and subtracting 21 from both sides, we get:

7 - 9x < 12 - 21

-2x < -9

Dividing both sides of the inequality by -2 (remembering to flip the inequality sign when dividing by a negative number), we have:

x > -9 / -2

x > 9/2

So the solution to the inequality 1/3 * (x + 3) < 1/7 * (3x + 4) is x > 9/2.

Graphically, the solution set is all real numbers greater than 9/2 represented by a shaded line extending to the right on the number line.

In interval notation, the solution is (9/2, ∞).