Eight times a number minus twenty-three is no more than the opposite of that number plus eighteen. find that number.

8x - 23 = -x + 18 is how I'm interpreting your query.

"the opposite of the number" is slightly confusing, so I'm assuming you mean a negative. If not, please let me know.

We can solve for x using this equation.

8x - 23 = 18 - x

Add x to both sides

9x - 23 = 18

Add 23 to both sides

9x = 41

Divide both sides by 9

x = 4.56

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: