Chapter 2: Q42. (page 101)

REASONING Solve the equation below. Describe each step.
$t = 2 - 2 [2 t - 3 (1 - t)]$

Short Answer

Expert verified

The solution of the given equation is $t = \frac{8}{11}$ .

Step by step solution

Step 1. Write the given equation.

The given equation is “ $t = 2 - 2 [2 t - 3 (1 - t)]$ ”.

Step 2. Solve the given equation.

Solving,

$t = 2 - 2 [2 t - 3 (1 - t)]$ (Given equation)

$t = 2 - 2 [2 t - 3 + 3 t]$ (Distributive property)

$t = 2 - 2 [5 t - 3]$ (Simplify)

$t = 2 - 10 t + 6$ (Distributive property)

$t = - 10 t + 8$ (Simplify)

$t + 10 t = - 10 t + 8 + 10 t$ (Add $10 t$ to both sides)

$11 t = 8$ (Simplify)

$\frac{11 t}{11} = \frac{8}{11}$ (Divide both sides by 11)

$t = \frac{8}{11}$ (Simplify)

So, $t = \frac{8}{11}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $t = \frac{8}{11}$ in the given equation $t = 2 - 2 [2 t - 3 (1 - t)]$ to get,

$\begin{array}{l} \frac{8}{11} = 2 - 2 [2 (\frac{8}{11}) - 3 (1 - \frac{8}{11})] \\ \frac{8}{11} = 2 - 2 [\frac{16}{11} - 3 (\frac{3}{11})] \\ \frac{8}{11} = 2 - 2 [\frac{16}{11} - \frac{9}{11}] \\ \frac{8}{11} = 2 - 2 [\frac{7}{11}] \end{array}$

On further simplification,

$\begin{array}{l} \frac{8}{11} = 2 - \frac{14}{11} \\ \frac{8}{11} = \frac{22 - 14}{11} \\ \frac{8}{11} = \frac{8}{11} \end{array}$

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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REASONING Solve the equation below. Describe each step.
$t = 2 - 2 [2 t - 3 (1 - t)]$

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

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REASONING Solve the equation below. Describe each step.t=2−22t−31−t

Short Answer

Step by step solution

Step 1. Write the given equation.

Step 2. Solve the given equation.

Step 3. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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REASONING Solve the equation below. Describe each step.
$t = 2 - 2 [2 t - 3 (1 - t)]$