Question

operations for solving equations with the variable on both sides - item 35006
solve each equation.
2k = - 3 + 7(k + 4)
k =
7y = 6 + 3(y + 2)
y =

Explanation:

Step1: Expand the right - hand side

First, expand \(7(k + 4)\) in the equation \(2k=-3 + 7(k + 4)\) using the distributive property \(a(b + c)=ab+ac\). So \(7(k + 4)=7k+28\), and the equation becomes \(2k=-3 + 7k+28\).

Step2: Combine like - terms

Combine the constant terms on the right - hand side: \(-3+28 = 25\), so the equation is \(2k=7k + 25\).

Step3: Move variable terms to one side

Subtract \(7k\) from both sides: \(2k-7k=7k + 25-7k\), which simplifies to \(-5k=25\).

Step4: Solve for \(k\)

Divide both sides by \(-5\): \(\frac{-5k}{-5}=\frac{25}{-5}\), so \(k=-5\).

Now for the equation \(7y = 6+3(y + 2)\):

Step1: Expand the right - hand side

Expand \(3(y + 2)\) using the distributive property. \(3(y + 2)=3y+6\), so the equation becomes \(7y=6 + 3y+6\).

Step2: Combine like - terms

Combine the constant terms on the right - hand side: \(6 + 6=12\), so the equation is \(7y=3y + 12\).

Step3: Move variable terms to one side

Subtract \(3y\) from both sides: \(7y-3y=3y + 12-3y\), which simplifies to \(4y=12\).

Step4: Solve for \(y\)

Divide both sides by \(4\): \(\frac{4y}{4}=\frac{12}{4}\), so \(y = 3\).

Answer:

For \(2k=-3 + 7(k + 4)\), \(k=-5\)
For \(7y = 6+3(y + 2)\), \(y = 3\)