Question

Are the equations -2x=10 and -5x=25 equivalent

Answer 1

To equations are equivalent if and only if they have the same solution set.

Solve for both of the equations.

-2x = 10
x = -5 <-- Divide both sides by -2

-5x = 25
x = -5 <-- Divide both sides by -5

Both have the solution -5.

So, yes both are equivalent.

Answer 2

The two equations ( -2x=10 and -5x=25) are equivalent, since the values of the unknown variables(x) in the two equations are equal.

To determine if the equations are equivalent, we will solve each of the equations.

These equations are examples of Linear equations.

NOTE: Linear equations are the equations of degree 1 (that is, the highest power of the unknown is 1)

To solve a linear equation, we will determine the value of the unknown (variable) that satisfies the equation.

For -2x = 10

$-2x = 10$

Divide both sides by -2

$\frac{-2x}{-2} = \frac{10}{-2}$

$x = -5$

∴ The value of the unknown in the equation (-2x=10) is x = -5

For -5x = 25

$-5x = 25$

Divide both sides by -5

$\frac{-5x}{-5} = \frac{25}{-5}$

$x = -5$

∴The value of the unknown in the equation (-5x=25) is x = -5

Since the values of the unknown variable(x) are equal in the two equations, then the two equations are equivalent.

Hence, the two equations ( -2x=10 and -5x=25) are equivalent, since the values of the unknown variables(x) in the two equations are equal.  

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