Step by step solution to "For exercise, solve the equations and inequalities. Write..."

Jason Farmer

Answered question

2021-10-22

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation.

\sqrt{t + 3} + 4 = t + 1

Faiza Fuller

Skilled2021-10-23Added 108 answers

On simplification, we get

\sqrt{t + 3} + 4 = t + 1

\Rightarrow \sqrt{t + 3} = t - 3

Squaring on both sides, we get

\Rightarrow {(\sqrt{t + 3})}^{2} = {(t - 3)}^{2}

\Rightarrow t + 3 = t^{2} - 6 t + 9

\Rightarrow t^{2} - 7 t + 6 = 0

\Rightarrow t^{2} - 6 t - t + 6 = 0

\Rightarrow t (t - 6) - (t - 6) = 0

\Rightarrow (t - 6) (t - 1) = 0

\Rightarrow t - 6 = 0 or t - 1 = 0

\Rightarrow t = 6 or t = 1

But the given equation cannot satisfy when

t = 1

∴ t = 6

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