Chapter 3: Q34. (page 133)

Solve the equation. Check your solution.
$3 x - 7 = 8 + 6 (x + 2)$

Short Answer

Expert verified

The solution for the equation $3 x - 7 = 8 + 6 (x + 2)$ is $x = - 9$ .

Step by step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{matrix} 3 x - 7 = 8 + 6 (x + 2) \\ 3 x - 7 = 8 + 6 x + 12 (Usedistributiveproperty) \\ 3 x - 6 x - 7 = 20 + 6 x - 6 x (Subtract6xfrombothsides) \\ - 3 x - 7 = 20 (Simplify) \\ - 3 x - 7 + 7 = 20 + 7 (Add7tobothsides) \\ - 3 x = 27 (Simplify) \end{matrix}$

– Solve for x

Now, divide both sides of the equation by -3.

$\begin{matrix} \frac{- 3 x}{- 3} = \frac{27}{- 3} \\ x = - 9 \end{matrix}$

Therefore, the solution of the equation is $x = - 9$ .

– Check the solution

To check the solution, write the original equation and substitute the value of x.

$3 x - 7 = 8 + 6 (x + 2)$

Now, substitute $x = - 9$ and check the result.

$\begin{matrix} 3 (- 9) - 7 = 8 + 6 (- 9 + 2) \\ - 27 - 7 = 8 + 6 (- 7) \\ - 34 = 8 - 42 \\ - 34 = - 34 \end{matrix}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.

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Solve the equation. Check your solution.
$3 x - 7 = 8 + 6 (x + 2)$

Short Answer

Step by step solution

– Separate the variable and constants

– Solve for x

– Check the solution

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Solve the equation. Check your solution.3x-7=8+6x+2

Short Answer

Step by step solution

– Separate the variable and constants

– Solve for x

– Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Calculus

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve the equation. Check your solution.
$3 x - 7 = 8 + 6 (x + 2)$