Question

solve for $x$ and graph the solution on the number line below.

$-5x - 7 < 3$ and $-5x - 7 > -42$

answer attempt 1 out of 2

$<$$>$$\leq$$\geq$or

inequality notation:

number line:

submit answer

Explanation:

Step1: Solve the first inequality

Solve \(-5x - 7\lt3\).
Add \(7\) to both sides: \(-5x-7 + 7\lt3 + 7\), which simplifies to \(-5x\lt10\).
Divide both sides by \(- 5\) (and reverse the inequality sign): \(x\gt - 2\).

Step2: Solve the second inequality

Solve \(-5x - 7\gt - 42\).
Add \(7\) to both sides: \(-5x-7 + 7\gt - 42+7\), which simplifies to \(-5x\gt - 35\).
Divide both sides by \(-5\) (and reverse the inequality sign): \(x\lt7\).

Answer:

Inequality Notation: \(-2\lt x\lt7\)

For the number - line:

• Place an open circle at \(x = - 2\) (because \(x\gt - 2\), the value \(-2\) is not included in the solution set).
• Place an open circle at \(x = 7\) (because \(x\lt7\), the value \(7\) is not included in the solution set).
• Draw a line segment connecting the two open circles.