Question Simplify the equation $6(x-5)+5=5(x-8)$ using distributive, equality, and inverse properties.

Studdy Solution

STEP 1

Assumptions
1. The equation to solve is $6(x-5)+5=5(x-8)$ .
2. We will use the distributive property to expand the terms.
3. We will use the addition principle of equality to isolate terms.
4. We will use the multiplication principle of equality to simplify terms.
5. We will use the additive inverse property to move terms from one side of the equation to the other.
6. We will use the division principle of equality to solve for $x$ .

STEP 2

Use the distributive property to expand the terms on both sides of the equation.
$6(x-5)+5=5(x-8)$
$6x - 6 \cdot 5 + 5 = 5x - 5 \cdot 8$

STEP 3

Simplify the expanded terms.
$6x - 30 + 5 = 5x - 40$

STEP 4

Combine like terms on each side of the equation.
$6x - 25 = 5x - 40$

STEP 5

Use the addition principle of equality to move the term $5x$ from the right side to the left side by subtracting $5x$ from both sides.
$6x - 5x - 25 = 5x - 5x - 40$

STEP 6

Simplify the equation after subtracting $5x$ from both sides.
$x - 25 = -40$

STEP 7

Use the addition principle of equality to move the constant term $-25$ from the left side to the right side by adding $25$ to both sides.
$x - 25 + 25 = -40 + 25$

STEP 8

Simplify the equation after adding $25$ to both sides.
$x = -15$
The solution to the equation $6(x-5)+5=5(x-8)$ is $x = -15$ .

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