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Chapter 6: Problem 47

Solve each inequality and graph the solution set on a number line. \(2 x-5>-x+6\)

Short Answer

Expert verified
The solution to the inequality \(2x - 5 > -x + 6\) is \(x > 3.67\). This can be represented on a number line as an open circle at \(3.67\) and a line shaded to the right of \(3.67\).

Step by step solution

01

Rearrange the inequality

To isolate 'x', first add 'x' from both sides of the inequality: \(2x + x > 5 + 6\) which simplifies to \(3x > 11\)
02

Solve the inequality

We can solve for 'x' by dividing both sides of the inequality by 3: \(x > 11/3\) which simplifies to \(x > 3.67\)
03

Graph the solution

From this inequality, we can interpret that 'x' is any number greater than \(3.67\). To represent this on a number line, draw an open circle at \(3.67\) (since 'x' is strictly greater than \(3.67\) and does not equal \(3.67\)), and shade the line to the right of \(3.67\) to denote all the numbers greater than it.

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