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Math

Question Find the values of xx where x+2>5−xx+2 > 5-x.

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality x+2>5−xx + 2 > 5 - x.
2. We need to solve for the values of xx that satisfy this inequality.

STEP 2

To solve the inequality x+2>5−xx + 2 > 5 - x, we want to isolate xx on one side of the inequality. We can start by adding xx to both sides to get all the xx terms on one side.
x+2+x>5−x+xx + 2 + x > 5 - x + x

STEP 3

Combine like terms on both sides of the inequality.
2x+2>52x + 2 > 5

STEP 4

Now, we subtract 2 from both sides of the inequality to isolate the term with xx.
2x+2−2>5−22x + 2 - 2 > 5 - 2

STEP 5

Simplify both sides of the inequality.
2x>32x > 3

STEP 6

To solve for xx, we divide both sides of the inequality by 2.
2x2>32\frac{2x}{2} > \frac{3}{2}

STEP 7

Simplify the inequality to find the solution for xx.
x>32x > \frac{3}{2}
The values of xx for which the inequality x+2>5−xx + 2 > 5 - x is true are all values greater than 32\frac{3}{2}.
The correct answer is: all values of xx greater than 32\frac{3}{2}.

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