Question

(\frac{2}{5}(x + 3) = -4(x - 1))

Explanation:

Step1: Eliminate fraction by multiplying both sides by 5

Multiply each term by 5 to get rid of the denominator: \(5\times\frac{2}{5}(x + 3)=5\times(-4)(x - 1)\)
Simplify: \(2(x + 3)=-20(x - 1)\)

Step2: Distribute both sides

Use distributive property \(a(b + c)=ab + ac\):
Left side: \(2x+6\)
Right side: \(-20x + 20\)
Equation: \(2x + 6=-20x + 20\)

Step3: Add \(20x\) to both sides

To get all \(x\) terms on left: \(2x+20x + 6=-20x+20x + 20\)
Simplify: \(22x + 6=20\)

Step4: Subtract 6 from both sides

Isolate \(x\) term: \(22x + 6 - 6=20 - 6\)
Simplify: \(22x=14\)

Step5: Divide by 22 and simplify

Divide both sides by 22: \(x=\frac{14}{22}\)
Simplify fraction: \(x=\frac{7}{11}\)

Answer:

\(x = \frac{7}{11}\)