What is sqrt(2a-3)<5 ?

The solution to sqrt(2a-3)<5 is 3/2 <= a<14

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sqrt(2a-3)<5

2 a - 3 < 5

\frac{3}{2} \leq a < 14

Interval Notation

[\frac{3}{2}, 14)

Decimal Notation

1.5 \leq a < 14

Solution steps

2 a - 3 < 5

Square both sides

(2 a - 3)^{2} < 5^{2}

Simplify

2 a - 3 < 25

2 a - 3 < 25 : a < 14

a < 14

Find singularity points

Find non-negative values for radicals:

a \geq \frac{3}{2}

Combine the intervals

a < 14 and a \geq \frac{3}{2}

Merge Overlapping Intervals

\frac{3}{2} \leq a < 14

x^{2} - 9 x + 24 = 0

- x \leq 2

x (m + 5) + 7 (m + 5)

5 - x = 6

\frac{x}{5} = 3