Page 641 - Algebra 1

Solving Equations with Operations Inside the Absolute-Value Symbols
Solve each equation.
a. ⎪2x⎥+9=15 SOLUTION
⎪2x⎥ + 9 = 15
⎪2x⎥ = 6 Subtract 9 from both sides.
Write the equation as two equations without the absolute value. Then solve
Example
3
both equations.
2x = 6 or
x = 3 Divide both sides by 2. The solution set is {3, -3}.
b. 6⎪x+3⎥-8=10 SOLUTION
6⎪x + 3⎥ - 8 = 10
6⎪x + 3⎥ = 18 Add 8 to both sides. ⎪x + 3⎥ = 3 Divide both sides by 6.
2x = -6 x = -3
Write the equation as two equations without the absolute value and solve.
Math Reasoning
Write Why do you
often have to solve
two equations without absolute value to find the solution to one equation with absolute value?
x + 3 = 3 or
x = 0 Subtract 3 from both sides.
x + 3 = -3 x = -6
The solution set is {0, -6}. c. 5 _x - 2 = 15
⎪3 ⎥ SOLUTION
5 _x - 2 = 1 5 ⎪3 ⎥
_x -2 =3 ⎪3 ⎥
Dividebothsidesby5.
Write the equation as two equations without the absolute value and solve.
_x - 2 = 3 o r _x - 2 = - 3 33
_x =5 Add2tobothsides. _x =-1 33
x = 15 Multiply both sides by 3. x = -3 The solution set is {15, -3}.
626 Saxon Algebra 1