Question

1. solve ( 16x - 8 - 9x = 27 ) 11. solve and graph ( 7x - 5 geq 65 ) or ( - 3x - 2 > - 2 )

Explanation:

Step1: Simplify the equation

Combine like terms in \(16x - 8 - 9x=27\).
\(16x-9x - 8=27\)
\(7x-8 = 27\)

Step2: Isolate the variable term

Add \(8\) to both sides of the equation.
\(7x-8 + 8=27 + 8\)
\(7x=35\)

Step3: Solve for \(x\)

Divide both sides by \(7\).
\(x=\frac{35}{7}=5\)

For the compound - inequality \(7x - 5\geq65\) or \(-3x - 2>-2\)

Solve \(7x - 5\geq65\)

Step1: Isolate the variable term

Add \(5\) to both sides: \(7x-5 + 5\geq65 + 5\)
\(7x\geq70\)

Step2: Solve for \(x\)

Divide both sides by \(7\): \(x\geq10\)

Solve \(-3x - 2>-2\)

Step1: Isolate the variable term

Add \(2\) to both sides: \(-3x-2 + 2>-2 + 2\)
\(-3x>0\)

Step2: Solve for \(x\)

Divide both sides by \(- 3\). When dividing by a negative number, reverse the inequality sign.
\(x<0\)

Answer:

For problem 10: \(x = 5\)
For problem 11: The solution of the compound - inequality is \(x<0\) or \(x\geq10\). On the number - line, we have an open circle at \(x = 0\) and shade to the left of \(0\), and a closed circle at \(x = 10\) and shade to the right of \(10\).