Decide if an equation has no solutions

Solve , if possible.

Example 4

53x + 6 =+ 2–

Write original equation.53x + 6 =+ 2–

Subtract 6 from each side.53x + = 8–

The absolute value of a number is never negative. So, there are no solutions.

ANSWER

Use absolute deviationExample 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 airpressures 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 deviationExample 5

Write original equation.0.5 = 8p –

or Rewrite as two equations.0.5 = 8p – = 8p –0.5–

or Add 8 to each side.8.5 = p = p7.5

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.

5m 4 =+ 2–2

9. 2n 7 =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–