Question

linear inequalities with decimals
question
solve the following inequality:
9x - 10 < 1.8 - 10(-x + 1)
answer
attempt 1 out of 2

Explanation:

Step1: Expand the right - hand side

We use the distributive property \(a(b + c)=ab+ac\). For \(- 10(-x + 1)\), we have \(-10\times(-x)+(-10)\times1 = 10x-10\). So the inequality \(9x - 10\lt1.8-10(-x + 1)\) becomes \(9x-10\lt1.8 + 10x-10\).

Step2: Simplify the right - hand side

Simplify \(1.8 + 10x-10\). Combine the constant terms: \(1.8-10=-8.2\). So the inequality is \(9x - 10\lt10x-8.2\).

Step3: Subtract \(9x\) from both sides

Subtract \(9x\) from each side of the inequality: \((9x - 10)-9x\lt(10x-8.2)-9x\). This simplifies to \(-10\lt x - 8.2\).

Step4: Add 8.2 to both sides

Add 8.2 to both sides of the inequality \(-10 + 8.2\lt x-8.2 + 8.2\). Calculate \(-10 + 8.2=-1.8\). So we get \(-1.8\lt x\), or \(x\gt - 1.8\).

Answer:

\(x\gt - 1.8\)