Question

Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2 What is the other solution to the equation? x=−6 x=−4 x=2 x=4

Answer 1

Answer:

x = - 4

Step-by-step explanation:

Given

3 - 2 |0.5x + 1.5 | = 2 ( subtract 3 from both sides )

- 2 |0.5x + 1.5 | = - 1 ( divide both sides by - 2 )

|0.5x + 1.5 | = 0.5

The absolute value function always gives a positive value, however, the expression inside can be positive or negative, thus

0.5x + 1.5 = 0.5 ( subtract 1.5 from both sides )

0.5x = - 1 ( divide both sides by 0.5 )

x = - 2 ← solution Manuela obtained

OR

-(0.5x + 1.5) = 0.5 ← distribute parenthesis on left side by - 1

- 0.5x - 1.5 = 0.5 ( add 1.5 to both sides )

- 0.5x = 2 ( divide both sides by - 0.5 )

x = - 4 ← other solution to the equation

Answer 2

Based on the information given, it can be noted that the solution to the equation will be x = -4.

Solving an equation.

From the equation given, 0.5x + 1.5 = 0.5

Subtract 1.5 from both sides

0.5x + 1.5 - 1.5 = 0.5 - 1.5

0.5x = - 1

Divide both side by 0.5

0.5x/0.5 = 1/0.5

x = 2

Also, the other solution will be:

-0.5x - 1.5 = 0.5

-0.5x = 0.5 + 1.5

-0.5x = 2

x = 2/-0.5

x = -4.

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