Question

Solve.

2x -3 > 23
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2x - 3 > 3x -1
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5x - 4 < 21
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x>-2 x<5. x>13. x<-2. x>5​

Answer 1

1. x > 13

2. x < -2

3. x < 5

Explanation:

2x - 3 > 23

→Add 3 to both sides:

2x > 26

→Divide both sides by 2:

x > 13

2x - 3 > 3x - 1

→Subtract 2x from both sides:

-3 > x - 1

→Add 1 to both sides:

-2 > x

5x - 4 < 21

→Add 4 to both sides:

5x < 25

→Divide both sides by 5:

x < 5

Answer 2

The correct combination of solutions is x > -2, x < 5, x > 13, as determined by the analysis of the inequalities.

2x - 3 > 23

Add 3 to both sides: 2x - 3 + 3 > 23 + 3

Simplify: 2x > 26

Divide by 2: x > 13

Solution: x > 13

2x - 3 > 3x - 1

Add 3 to both sides: 2x - 3 + 3 > 3x - 1 + 3

Simplify: 2x > 3x + 2

Subtract 3x from both sides: 2x - 3x > 2

Simplify: -x > 2

Multiply by -1 (reverse inequality): x < -2

Solution: x < -2

5x - 4 < 21

Add 4 to both sides: 5x - 4 + 4 < 21 + 4

Simplify: 5x < 25

Divide by 5: x < 5

Solution: x < 5

x > -2: True based on the solution from the second inequality.

x < 5: True based on the solution from the third inequality.

x > 13: True based on the solution from the first inequality.

x < -2: True based on the solution from the second inequality.

x > 5: Not true based on the solution from the third inequality.

Therefore, the correct combination is x > -2, x < 5, x > 13.