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Identify linear and non-linear equations.

Linear

Non-Linear

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x=6+3x\sqrt{x}=6+3x
x
​
=6+3x

2x+7x=−32x+7x=-32x+7x=−3

7x−6=37x-6=37x−6=3

2x4+−3x=52x^{4}+-3x=52x
4
+−3x=5

3 answers

Here are the classifications of the given equations:

Linear:

  1. \( 2x + 7 = -3 \)
  2. \( 7x - 6 = 3 \)

Non-Linear:

  1. \( x = 6 + 3x \)
  2. \( 2x^4 - 3x = 5 \)

Explanation:

  • Linear equations are characterized by the highest power of the variable being 1.
  • Non-linear equations involve terms where the variable is raised to a power greater than 1 or involves roots, products, etc.

In this case, it appears that the equation \( x = 6 + 3x \) is rewritten but is actually solvable as linear since it simplifies to \( -2x + 6 = 0 \), so it would technically also be linear. However, we include it here because it initially has a non-standard form that involves isolation of \( x \) on both sides.

Let me know if there's anything else you need!

Solve the following linear equation.

−5x−10=18-5x-10=18−5x−10=18

x=x=x=

To solve the linear equation \(-5x - 10 = 18\), follow these steps:

  1. Start with the equation: \[ -5x - 10 = 18 \]

  2. Add 10 to both sides of the equation: \[ -5x = 18 + 10 \] \[ -5x = 28 \]

  3. Now, divide both sides by \(-5\): \[ x = \frac{28}{-5} \] \[ x = -\frac{28}{5} \]

So the solution to the equation is: \[ x = -\frac{28}{5} \quad \text{or} \quad x = -5.6 \]