Question

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

( -5x + 7 > 47 ) or ( -5x + 7 leq -43 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Solve the first inequality

Subtract \(7\) from both sides of \(-5x + 7>47\):
\(-5x+7 - 7>47 - 7\)
\(-5x>40\)
Divide both sides by \(- 5\) and reverse the inequality sign (since dividing by a negative number):
\(x<-8\)

Step2: Solve the second inequality

Subtract \(7\) from both sides of \(-5x + 7\leq - 43\):
\(-5x+7 - 7\leq - 43 - 7\)
\(-5x\leq - 50\)
Divide both sides by \(-5\) and reverse the inequality sign:
\(x\geq10\)

Answer:

Inequality Notation: \(x < - 8\) or \(x\geq10\)

For the number - line:

• Plot an open circle at \(x = - 8\) and shade to the left (for \(x < - 8\)).
• Plot a closed circle at \(x = 10\) and shade to the right (for \(x\geq10\)).