Question

I need help with this

Answer 1

s = -24

Explanation:

This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.

Solution

Step 1

Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.

`7 = (1)/(6)s+11\qquad\text{given}\\\\7-11=(1)/(6)s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=(1)/(6)s\qquad\text{simplify}`

Step 2

Multiply both sides by the inverse of the coefficient of the variable.

`(6)(-4)=(6)\left((1)/(6)s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}`

Alternate solution

Often, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.

Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.

`7=(1)/(6)s+11\qquad\text{given}\\\\6(7)=6\left((1)/(6)s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}`

You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.

Check

The value we found for the variable can be checked in the original equation.

`7=(1)/(6)(-24)+11\\\\7=-4+11\qquad\text{true}`