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1< 3x-2 is less than or equal to 10

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2 Answers

we will write the inequality in a compact form since it is intersection case

1< 3x - 2 ≤ 10

3 < 3x ≤ 12    by adding 2 to all sides

1 < x ≤ 4    by dividing all sides by 3

( 1 , 4 ]  the answer written in interval notation

 

I am going to begin by separating this problem into two separate inequalities:

1 < 3x - 2 and 3x - 2 ≤10

We will solve these separately

1 < 3x -2                   Given

1 + 2 < 3x - 2 + 2      Add 2 to each side

3 < 3x                       Simplify each side

1 < x                        Divide each side by 3

Now we will solve the second inequality

3x - 2 ≤ 10               Given

3x - 2 + 2 ≤ 10 + 2    Add 2 to each side

3x ≤ 12                    Simplify each side

x ≤ 4                        Divide each side by 4

We can now combine the answers of the two inequalities into one statement:

1 < x ≤ 4