Question

solve for ( x ) and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (( varnothing )), leave the number line blank.

( 13 < 4x + 9 ) and ( 4x + 9 geq 37 )

answer attempt 1 out of 5

inequality notation:

number line:

Explanation:

Step1: Solve \(13 < 4x + 9\)

Subtract 9 from both sides: \(13 - 9 < 4x + 9 - 9\)
Simplify: \(4 < 4x\)
Divide both sides by 4: \(\frac{4}{4} < \frac{4x}{4}\)
Simplify: \(1 < x\) or \(x > 1\)

Step2: Solve \(4x + 9 \geq 37\)

Subtract 9 from both sides: \(4x + 9 - 9 \geq 37 - 9\)
Simplify: \(4x \geq 28\)
Divide both sides by 4: \(\frac{4x}{4} \geq \frac{28}{4}\)
Simplify: \(x \geq 7\)

Step3: Find the intersection

We have \(x > 1\) and \(x \geq 7\). The intersection of these two inequalities is \(x \geq 7\) (since \(x \geq 7\) is a subset of \(x > 1\)).

Answer:

Inequality Notation: \(x \geq 7\)
Number Line: (To graph \(x \geq 7\) on a number line, draw a closed circle at 7 and shade to the right of 7.)