Question

Solve the linear inequality. Express the solution using set-builder notation and interval notation. Graph the solution set. - 7x+4> 46 Express the solution in set-builder notation. Choose the correct answer below. O A. The solution set is {x}. (Use integers or fractions for any numbers in the expression.) B. The solution is all real numbers. OC. The solution is the empty set.

Answer 1

The solution to the inequality -7x + 4 > 46 is x < -6. In set-builder notation, this is {x: x < -6}, and in interval notation it is (-∞, -6). The graph shows an open dot at -6, with the line heading towards negative infinity.

To solve the inequality -7x + 4 > 46, we first want to isolate the term with 'x' in it. We can do so by subtracting 4 from both sides of the inequality, which gives us -7x > 42. Then, we divide both sides by -7. However, when we divide or multiply an inequality by a negative number, we must reverse the inequality symbol. Therefore, our inequality becomes x < -6.

In set-builder notation, this would be expressed as {x: x < -6}. In interval notation, we write this as (-∞, -6). The graph of this solution set is a number line where x can be any number less than -6. The line is going towards negative infinity and it has an open dot at -6, indicating that -6 is not included in the solution set.

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