Question

1. 2(3x + 8) = 2x + 16 + 4x
2. 3(4x + 2) = 20x - 9x + 2
3. 8(2x + 5) = 16x + 40

Explanation:

Step1: Expand left - hand side of equation 3

Use distributive property \(a(b + c)=ab+ac\). So, \(2(3x + 8)=2\times3x+2\times8 = 6x+16\). The right - hand side is \(2x + 16+4x=6x + 16\). Since \(6x+16=6x + 16\) for all real \(x\), the solution is all real numbers.

Step2: Expand left - hand side of equation 5

Using distributive property, \(3(4x + 2)=3\times4x+3\times2=12x + 6\). The right - hand side is \(20x-9x + 2=11x+2\). Then, set up the equation \(12x + 6=11x+2\). Subtract \(11x\) from both sides: \(12x-11x+6=11x-11x + 2\), which gives \(x+6=2\). Subtract 6 from both sides: \(x=2 - 6=-4\).

Step3: Expand left - hand side of equation 7

By distributive property, \(8(2x + 5)=8\times2x+8\times5=16x + 40\). The right - hand side is \(16x + 40\). Since \(16x+40=16x + 40\) for all real \(x\), the solution is all real numbers.

Answer:

For equation 3: All real numbers
For equation 5: \(x=-4\)
For equation 7: All real numbers