Question

question
solve for x and graph the solution on the number line below.
-3 ≥ -4 + x
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Isolate the variable \(x\)

Add \(4\) to both sides of the inequality \(-3\geq - 4+x\).
Using the addition property of inequalities (\(a\geq b\) implies \(a + c\geq b + c\)), we get \(-3 + 4\geq-4 + x+4\).
Simplify the left - hand side: \(\frac{-3 + 4}{1}\geq x\), which is \(1\geq x\).

Step2: Rewrite the inequality

The inequality \(1\geq x\) can be rewritten as \(x\leq1\).

Answer:

Inequality Notation: \(x\leq1\)

To graph \(x\leq1\) on the number line:

• Place a closed circle at \(x = 1\) (because the inequality includes equality, i.e., \(x\) can be equal to \(1\)).
• Shade the line to the left of \(1\) (since \(x\) is less than or equal to \(1\)).