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Chapter 2: Q. 6 (page 126)

Find the real solutions of the equation:
$\sqrt{2 x + 3} = 2$

Short Answer

Expert verified

The solution of the given equation is

$x = \frac{1}{2}$

Step by step solution

01

Step 1. Given information

The given information is $\sqrt{2 x + 3} = 2$

02

Step 2. Squaring both sides

Squaring both sides to the equation, we get:

${(\sqrt{2 x + 3})}^{2} = 2^{2} 2 x + 3 = 4$

03

Step 3. Solving the equation

Solving the equation, we get:

$2 x + 3 = 4 2 x = 1 x = \frac{1}{2}$

04

Step 4. Verify the solution

Substituting $x = \frac{1}{2}$ in the equation we get:

$\sqrt{2 x + 3} = 2 \sqrt{2 \times \frac{1}{2} + 3} = 2 \sqrt{1 + 3} = 2 \sqrt{4} = 2 2 = 2$

This is true.

Thus, the solution of the equation is:

$x = \frac{1}{2}$ .

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Most popular questions from this chapter

A wire $10$ meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.

Part (b): What is the domain of A?

Part (c): Graph $A = A (x)$ . For what value of xis Asmallest?

Write the point–slope form of the line with slope 5 containing the point (3, -2).

Exploration Graph $y = \sqrt{x}$ . Then on the same screen graph $y = \sqrt{- x}$ . What pattern do you observe? Now try $y = 2 x + 1$ and $y = 2 (- x) + 1$ . What do you conclude?

In Problems 7–18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

True or False The cube function is odd and is increasing on the interval $(- \infty, \infty)$ .

See all solutions

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