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Chapter 2: Q42. (page 101)

REASONING Solve the equation below. Describe each step.

t=2鈭�22t鈭�31鈭�t

Short Answer

Expert verified

The solution of the given equation is t=811.

Step by step solution

01

Step 1. Write the given equation.

The given equation is 鈥�t=2鈭�22t鈭�31鈭�t鈥�.

02

Step 2. Solve the given equation.

Solving,

t=2鈭�22t鈭�31鈭�t (Given equation)

t=2鈭�22t鈭�3+3t (Distributive property)

t=2鈭�25t鈭�3 (Simplify)

t=2鈭�10t+6 (Distributive property)

t=鈭�10t+8 (Simplify)

t+10t=鈭�10t+8+10t (Add 10tto both sides)

11t=8 (Simplify)

11t11=811 (Divide both sides by 11)

t=811 (Simplify)

So, t=811is the solution of the given equation.

03

Step 3. Check the obtained solution.

Put t=811in the given equation t=2鈭�22t鈭�31鈭�tto get,

811=2鈭�22811鈭�31鈭�811811=2鈭�21611鈭�3311811=2鈭�21611鈭�911811=2鈭�2711

On further simplification,

811=2鈭�1411811=22鈭�1411811=811

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.

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