Question

what is the solution to the linear equation?
$d - 10 - 2d + 7 = 8 + d - 10 - 3d$
options: $d = 1$, $d = -1$, $d = 5$, $d = -5$

Explanation:

Step1: Simplify both sides

Left side: \(d - 10 - 2d + 7 = (d - 2d)+(-10 + 7)=-d - 3\)
Right side: \(8 + d - 10 - 3d=(d - 3d)+(8 - 10)=-2d - 2\)

Step2: Solve for \(d\)

Equation becomes \(-d - 3=-2d - 2\)
Add \(2d\) to both sides: \(-d + 2d - 3=-2d + 2d - 2\) → \(d - 3=-2\)
Add 3 to both sides: \(d - 3 + 3=-2 + 3\) → \(d = 1\)

Answer:

\(d = 1\)