Decide if an equation has no solutions Solve, if possible. Example 4 53x3x + 6 = + 2 – Write original equation. 53x3x + 6 = + 2 – Subtract 6 from each side. 53x3x + = 8 – The absolute value of a number is never negative. So, there are no solutions. ANSWER

Use absolute deviation Example 5 Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of 0.5 psi. Find the minimum and maximum acceptable air pressures for the basketball. BASKETBALLS Let p be the air pressure (in psi) of a basketball. Write a verbal model. Then write and solve an absolute value equation. SOLUTION

Use absolute deviation Example 5 Write original equation. 0.5 = 8p – or Rewrite as two equations. 0.5 = 8p – = 8p – – or Add 8 to each side. 8.5 = p = p 7.5 The minimum and maximum acceptable pressures are 7.5 psi and 8.5 psi. ANSWER

Guided Practice for Examples 4 and 5 8. Solve the equation, if possible. 5m4 = + 2 – n7 = 3 – + – 10 – 10. An NCAA football must be inflated to an air pressure of 13 psi with an absolute error of 0.5 psi. Find the minimum and maximum acceptable air pressures for an NCAA football. FOOTBALL ANSWER no solution ANSWER 12.5 psi, 13.5 psi ANSWER 1, – 3 –