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In this lesson, we will learn how to solve equations involving the absolute value.

Q1:

What is the solution set of the equation | π₯ | = 9 4 ?

Q2:

What is the solution set of the equation | π₯ | = 4 8 ?

Q3:

What is the solution set of the equation | π₯ | = 6 5 ?

Q4:

What is the solution set of the equation | π₯ | = 5 9 ?

Q5:

What is the solution set of the equation ?

Q6:

Q7:

Find the solution set of the equation | π₯ + 3 | = β 3 π₯ + 7 .

Q8:

Find the solution set of the equation | π₯ + 8 | = β 8 π₯ β 1 .

Q9:

Find the solution set of | π₯ + 3 | = | 2 π₯ β 6 | .

Q10:

Find the solution set of | 6 π₯ + 8 | = | β 4 π₯ β 2 | .

Q11:

Amir was selling DVDs. The prices of the DVDs can be described by the equation | π β 1 5 | = 4 where π is the price in dollars. By graphing the equation π¦ = | π₯ β 1 5 | or otherwise, determine the highest and the lowest cost of a DVD.

Q12:

Solve | π₯ | + 1 2 = 1 8 .

Q13:

Find algebraically the solution set of the equation | π₯ + 4 | = π₯ + 4 .

Q14:

Find algebraically the solution set of the equation | π₯ + 1 0 | = π₯ + 1 0 .

Q15:

Write an equation that represents the following: 19 times the absolute value of a number is equal to 323.

Q16:

Find the solution set of the equation β 1 0 β β 2 8 π₯ = | β 1 8 | in β .

Q17:

Find algebraically the solution set of the equation 4 π₯ | π₯ | β 4 π₯ = 0 .

Q18:

Find algebraically the solution set of the equation | π₯ + 3 | | π₯ β 3 | = 3 9 .

Q19:

Given that 2 Γ | β 1 2 | = 2 Γ | π₯ + 1 | , find the value of π₯ .

Q20:

Find the solution set of 6 π₯ + 2 2 = | β 4 | in β .

Q21:

Find algebraically in β the solution set of the equation | π₯ Β± π | = β | π₯ Β± π | , where π is constant.

Q22:

If | β 6 | Γ π₯ = β 6 6 , what is the value of π₯ ?

Q23:

Find the solution set of β 7 π₯ = | β 3 5 | in β .

Q24:

Find all possible values of π₯ given | | | π₯ β 5 6 | | | = 5 6 .

Q25:

Given that π > 0 , find the solution set of the equation | π₯ | + π = 0 .

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