Question

Solve the inequality. \(x+3 \leq 2(x-4)\)

Short answer

The solution to the inequality is \(x \geq 11\).

Step-by-step solution

Distribute 2 on the right hand side

Multiply 2 by every term inside the brackets in the right side of the inequality. This gives \(x+3 \leq 2x-8\)

Subtract \(x\) from both sides

To isolate \(x\), subtract \(x\) from both sides of the equation. This results in \(3 \leq x - 8\).

Add 8 to both sides

Further isolating \(x\), add 8 to both sides of the equation. Giving us the final inequality \(x \geq 11\).