solve the equation 2(x + 1)=5(x - 3)-1. be sure to check your proposed solution by substituting it for the…

solve the equation 2(x + 1)=5(x - 3)-1. be sure to check your proposed solution by substituting it for the variable in the original equation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is { }. (type an integer or a simplified fraction.) b. all real numbers are solutions. c. the equation has no solution.

solve the equation 2(x + 1)=5(x - 3)-1. be sure to check your proposed solution by substituting it for the variable in the original equation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is { }. (type an integer or a simplified fraction.) b. all real numbers are solutions. c. the equation has no solution.

Answer

Explanation:

Step1: Expand both sides

Expand (2(x + 1)) to (2x+2) and (5(x - 3)-1) to (5x-15 - 1=5x-16). So the equation becomes (2x + 2=5x-16). [2(x + 1)=2x+2] [5(x - 3)-1=5x-15 - 1=5x-16]

Step2: Move (x) - terms to one side

Subtract (2x) from both sides: (2x+2-2x=5x - 16-2x), which simplifies to (2 = 3x-16). [2x+2-2x=5x - 16-2x] [2=3x - 16]

Step3: Isolate the (x) - term

Add 16 to both sides: (2 + 16=3x-16+16), getting (18 = 3x). [2+16=3x-16+16] [18=3x]

Step4: Solve for (x)

Divide both sides by 3: (\frac{18}{3}=\frac{3x}{3}), so (x = 6). [\frac{18}{3}=\frac{3x}{3}] [x = 6]

Step5: Check the solution

Substitute (x = 6) into the original equation: Left - hand side: (2(6 + 1)=2\times7 = 14). Right - hand side: (5(6 - 3)-1=5\times3-1=15 - 1=14). Since the left - hand side equals the right - hand side, (x = 6) is the solution.

Answer:

A. The solution set is ({6})