Decide if an equation has no solutions EXAMPLE 4 3x + 5 + 6 = –2 Write original equation. 3x + 5 = –8 Subtract 6 from each side. ANSWER The absolute value.

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Presentation transcript:

Decide if an equation has no solutions EXAMPLE 4 3x = –2 Write original equation. 3x + 5 = –8 Subtract 6 from each side. ANSWER The absolute value of a number is never negative. So, there are no solutions. 3x = –2, if possible.Solve

Use absolute deviation EXAMPLE 5 BASKETBALLS 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. (Absolute error is the absolute deviation of a measured value from an accepted value.) Find the minimum and maximum acceptable air pressures for the basketball.

Use absolute deviation EXAMPLE 5 SOLUTION Let p be the air pressure ( in psi ) of a basketball. Write a verbal model. Then write and solve an absolute value equation. 0.5=p–8

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

GUIDED PRACTICE for Examples 4 and 5 ANSWER no solution 5. 2 m – = 2 Solve the equation, if possible

GUIDED PRACTICE for Examples 4 and 5 6. –3 n +2 –7 = –10 Solve the equation, if possible ANSWER  1,  3

GUIDED PRACTICE for Examples 4 and 5 7. The absolute deviation of x from 7.6 is 5.2. What are the values of x that satisfy this requirement ? 12.8, 2.4 ANSWER