Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ -(d-3)=2(3 d+1) $$

Short answer

-0.20

Step-by-step solution

Distribute

First, apply the distributive property on the right side of the equation. Multiply each term inside the parentheses by 2. This will result in: \[ -(d-3) = 6d + 2 \]

Simplify the left side

Simplify the left side of the equation by distributing the negative sign to \(d\) and \(3\). This will change the -d to positive and the 3 to negative. Result will be: \[ d - 3 = 6d + 2 \]

Collect like terms

In order to isolate 'd', subtract \(d\) from both sides and subtract 2 from both sides. This will yield: \[ 2 - 3 = 6d - d \] which simplifies to: \[ -1 = 5d \]

Solve for 'd'

Finally, divide by 5 on both sides to solve for 'd': \[ d = -1 / 5 \]

Round the answer

The result in decimal form is -0.2. In order to round to the nearest hundredth, the result is: \[ -0.20 \]