Question

4. Noah is solving the inequality 7x + 5 > 2x + 35. First, he solves theequation 7x + 5 = 2x + 35 and gets x = 6. How does the solution to theequation 7x + 5 = 2x + 35 help Noah solve the inequality 7x + 5 > 2x + 35?Explain your reasoning.

Answer 1

Given the inequality below

$7x+5>2x+35$

Noah first solved the equation by changing the inequality sign to the equality sign as shown below

$\begin{gathered} 7x+5=2x+35 \\ \text{Collect like terms} \\ 7x-2x=35-5 \\ 5x=30 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{30}{5} \\ x=6 \end{gathered}$

Noah got x = 6

Solving the given inequality given

$\begin{gathered} 7x+5>2x+35 \\ \text{Collect like terms} \\ 7x-2x>35-5 \\ 5x>30 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}>\frac{30}{5} \\ x>6 \end{gathered}$

The solution to the inequality is x > 6

The solution to the first equation helped Noah in knowing the starting point of the solution to the inequality.

While the inequality sign helped Noah deduce whether the value of x is less than or greater than the solution to the first equation Noah solved