Question

solve for x and graph the solution on the number line below. -5x - 7 < 3 and -5x - 7 > -42 answer attempt 2 out of 10 inequality notation: x > -2 < 7 number line:

Explanation:

Step1: Solve the first - inequality

Add 7 to both sides of $-5x - 7<3$:
$-5x-7 + 7<3 + 7$, which simplifies to $-5x<10$. Then divide both sides by - 5. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $x>-2$.

Step2: Solve the second - inequality

Add 7 to both sides of $-5x - 7>-42$:
$-5x-7 + 7>-42 + 7$, which simplifies to $-5x>-35$. Divide both sides by - 5. Since we are dividing by a negative number, the inequality sign changes, and we get $x < 7$.

Answer:

Inequality Notation: $-2Number Line: Draw a number line. Mark an open - circle at $x=-2$ (because $x$ is greater than - 2, not equal to) and an open - circle at $x = 7$ (because $x$ is less than 7, not equal to). Then shade the region between the two open - circles.