Chapter 2: Q 2.2 (page 99)

Determine whether the values are solutions to the equation: $4 x - 2 = 2 x + 1$ .
(a) $x = \frac{3}{2}$ (b) $x = - \frac{1}{2}$

Short Answer

Expert verified

Part (a) $x = \frac{3}{2}$ is a solution to the equation.

Part (b) $x = - \frac{1}{2}$ is not a solution to the equation.

Step by step solution

Part (a) Step 1. Given information.

Determine whether the values are solutions to the equation: $4 x - 2 = 2 x + 1$ .

(a) $x = \frac{3}{2}$ (b) $x = - \frac{1}{2}$

Part (a) Step 2. Substitute the value x=32 in the equation.

$4 x - 2 = 2 x + 1 4 (\frac{3}{2}) - 2 = 2 (\frac{3}{2}) + 1 2 \cdot 3 - 2 = 1 \cdot 3 + 1 6 - 2 = 3 + 1 4 = 4$

Thus $x = \frac{3}{2}$ result in a true equation.

Hence, $x = \frac{3}{2}$ is a solution of the equation.

Part (b) Step 3. Substitute the value x=-12 in the equation.

$4 x - 2 = 2 x + 1 4 (- \frac{1}{2}) - 2 = 2 (- \frac{1}{2}) + 1 2 \cdot (- 1) - 2 = 1 \cdot (- 1) + 1 - 2 - 2 = - 1 + 1 - 4 \neq 0$

Thus $x = - \frac{1}{2}$ does not result in a true equation.

Hence, $x = - \frac{1}{2}$ is not a solution of the equation.

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Determine whether the values are solutions to the equation: $4 x - 2 = 2 x + 1$ .
(a) $x = \frac{3}{2}$ (b) $x = - \frac{1}{2}$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Substitute the value x=32 in the equation.

Part (b) Step 3. Substitute the value x=-12 in the equation.

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Determine whether the values are solutions to the equation: 4x-2=2x+1.(a)x=32(b)x=-12

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Substitute the value x=32 in the equation.

Part (b) Step 3. Substitute the value x=-12 in the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Calculus

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Determine whether the values are solutions to the equation: $4 x - 2 = 2 x + 1$ .
(a) $x = \frac{3}{2}$ (b) $x = - \frac{1}{2}$