Question

solve the inequality for x.
5(2x + 7) > 2x + 3
simplify your answer as much as possible

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(5(2x + 7)\) to get \(10x+35\). So the inequality becomes \(10x + 35>2x+3\).

Step2: Subtract \(2x\) from both sides

Subtracting \(2x\) from both sides of the inequality \(10x + 35>2x+3\) gives \(10x-2x + 35>2x-2x+3\), which simplifies to \(8x+35>3\).

Step3: Subtract 35 from both sides

Subtracting 35 from both sides of \(8x+35>3\) gives \(8x+35 - 35>3 - 35\), which simplifies to \(8x>- 32\).

Step4: Divide both sides by 8

Dividing both sides of \(8x>-32\) by 8 (since 8 is positive, the inequality sign remains the same) gives \(\frac{8x}{8}>\frac{-32}{8}\), which simplifies to \(x>-4\).

Answer:

\(x > - 4\)