QuestionIs the equation $-5(2 x-1)=-10 x+5$ an identity or does it have no solutions?

Studdy Solution

STEP 1

Assumptions1. The equation provided is $-5(x-1)=-10x+5$ . An identity is an equation that is true for all values of the variable3. If the equation is not an identity, it may have no solution if the left and right sides are not equal for any value of the variable

STEP 2

First, we simplify the left side of the equation by distributing the $-5$ across $(2x-1)$ .
$-5(2x-1) = -5 \cdot2x + -5 \cdot -1$

STEP 3

Now, calculate the values after the distribution.
$-5(2x-1) = -10x +5$

STEP 4

Now, we compare the simplified left side of the equation with the right side of the equation.
$-10x + = -10x +$

STEP 5

Since the left side of the equation is equal to the right side of the equation for all values of $x$ , we can conclude that the equation is an identity.
The equation $-5(2x-1)=-10x+5$ is an identity.

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