Math

Question Solve the inequality 3(x9)<153(x-9)<15 and select the correct answer.

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality 3(x9)<153(x-9)<15.
2. We need to solve for the variable xx.
3. The solution will be one of the given options.

STEP 2

First, we need to distribute the 33 across the parentheses to simplify the left side of the inequality.
3(x9)=3x393(x-9) = 3 \cdot x - 3 \cdot 9

STEP 3

Carry out the multiplication to simplify the expression.
3x39=3x273 \cdot x - 3 \cdot 9 = 3x - 27

STEP 4

Now the inequality looks like this:
3x27<153x - 27 < 15

STEP 5

Next, we need to isolate the variable xx on one side of the inequality. We can do this by adding 2727 to both sides of the inequality to cancel out the 27-27 on the left side.
3x27+27<15+273x - 27 + 27 < 15 + 27

STEP 6

Simplify both sides of the inequality.
3x<423x < 42

STEP 7

Now, we need to divide both sides of the inequality by 33 to solve for xx.
3x3<423\frac{3x}{3} < \frac{42}{3}

STEP 8

Carry out the division to find the value of xx.
x<14x < 14

STEP 9

The solution to the inequality 3(x9)<153(x-9)<15 is x<14x<14. Therefore, the correct answer is:
A) x<14x<14

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