Question

question
solve for ( x ) and graph the solution on the number line below.
( 10 leq -x + 7 ) or ( -x + 7 < 6 )
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Solve the first inequality \(10\leq -x + 7\)

Subtract 7 from both sides:
\(10-7\leq -x+7 - 7\)
\(3\leq -x\)
Multiply both sides by - 1 and reverse the inequality sign:
\(x\leq - 3\)

Step2: Solve the second inequality \(-x + 7\lt6\)

Subtract 7 from both sides:
\(-x+7 - 7\lt6 - 7\)
\(-x\lt - 1\)
Multiply both sides by - 1 and reverse the inequality sign:
\(x\gt1\)

Answer:

Inequality Notation: \(x\leq - 3\) or \(x\gt1\)

For the number - line:

• For \(x\leq - 3\), draw a closed circle at \(x = - 3\) and shade to the left.
• For \(x\gt1\), draw an open circle at \(x = 1\) and shade to the right.