Question

directions
select up to 2 number line button(s) below. click to activate and drag the circles on the number line to graph the answer
this question is calculator active
graph the solution set for ( 5 ( 6 + 3 x ) + 7 geq 127 )
select a ray. move the point on the ray to the correct place on the number line.

Explanation:

Step1: Solve the inequality

First, expand the left - hand side of the inequality \(5(6 + 3x)+7\geq127\).
Using the distributive property \(a(b + c)=ab+ac\), we get \(5\times6+5\times3x + 7\geq127\), which simplifies to \(30+15x+7\geq127\).
Combine like terms: \(15x + 37\geq127\).
Subtract 37 from both sides: \(15x+37 - 37\geq127 - 37\), so \(15x\geq90\).
Divide both sides by 15: \(x\geq\frac{90}{15}\), and \(x\geq6\).

Step2: Graph the solution on the number line

Since \(x\geq6\), we use a closed circle (because the inequality includes equality, i.e., \(x\) can be equal to 6) and draw a ray to the right (because \(x\) is greater than or equal to 6).

Answer:

On the number line, we should use the second button (the one with a closed circle and an upward - pointing arrow) and place the closed circle at \(x = 6\) (assuming the number line has appropriate markings for \(x = 6\)).