Final answer:
To find the value of b, first solve the equation 2x + 7 = 3 for x, which gives x = -2. Next, substitute this value into the equation bx - 10 = -2, and solve for b, which leads to the value of b being -4.
Step-by-step explanation:
To find the value of b for the equation bx - 10 = -2 that has the same solution as the equation 2x + 7 = 3, we first solve the second equation to find x.
Subtract 7 from both sides of the equation 2x + 7 = 3 to get 2x = -4. Then, divide both sides by 2 to find the value of x which gives x = -2. Now that we have the value of x, we substitute it into the first equation bx - 10 = -2. This leads to b(-2) - 10 = -2. Adding 10 to both sides gives us b(-2) = 8. Finally, divide both sides by -2 to solve for b, which gives us b = -4.
Thus, the value of b is -4.