Math

Question Find the range of values for xx that satisfy the inequality 2(x+8)>182(x+8)>18.

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality 2(x+8)>182(x+8)>18.
2. We need to solve for the variable xx.
3. The solution will be in the form of an inequality indicating the range of values that xx can take.

STEP 2

First, we need to simplify the inequality by distributing the 2 across the terms inside the parentheses.
2(x+8)>182(x+8)>18

STEP 3

Multiply 2 by each term inside the parentheses.
2x+28>182 \cdot x + 2 \cdot 8 > 18

STEP 4

Perform the multiplication.
2x+16>182x + 16 > 18

STEP 5

Now, we need to isolate the variable xx on one side of the inequality. We can do this by subtracting 16 from both sides of the inequality.
2x+1616>18162x + 16 - 16 > 18 - 16

STEP 6

Simplify both sides of the inequality.
2x>22x > 2

STEP 7

To solve for xx, we need to divide both sides of the inequality by 2.
2x2>22\frac{2x}{2} > \frac{2}{2}

STEP 8

Simplify both sides of the inequality.
x>1x > 1
The solution to the inequality 2(x+8)>182(x+8)>18 is x>1x > 1.

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