Final answer:
To make the equation 4(x+3)+5=109 equal -23, we need to first simplify and solve for x, then adjust the original equation by adding a negative component - in this case, subtract 46 - to achieve the desired outcome.
Step-by-step explanation:
To make the equation 4(x+3)+5=109 equal -23 instead of a positive 23, we need to change the given equation to match the desired outcome. Begin by simplifying the equation as follows:
• Subtract 5 from both sides of the equation to isolate the term with the variable:
• 4(x+3) = 109 - 5
• 4(x+3) = 104
Divide both sides by 4 to further isolate (x+3):
• x+3 = 104 / 4
• x+3 = 26
Finally, subtract 3 from both sides to solve for x:
• x = 26 - 3
• x = 23
However, since the goal is to make the equation result in -23, we'll need to incorporate a negative, either by subtracting 46 from both sides or including a multiplication by -1. If we subtract 46 from both sides, we have:
• x = 23 - 46
• x = -23
To achieve this with the original equation, we could subtract an additional 46 after dividing by 4:
• x + 3 = (104 / 4) - 46
• x + 3 = 26 - 46
• x = -23 - 3
• x = -26
Substituting x back into the original equation:
• 4(-26+3)+5 = 4(-23)+5
• = -92+5
• = -87
Note that to equal exactly -23, we must adjust the equation beforehand as the operations used only allow the left-hand side to reach -87 rather than -23.