Solve the equation. Check your answer.(Simplify your answer. Type an integer or a fraction.)
-4(r+7)=-79
r=
r = 18
To solve the equation -4(r+7) = -79, we need to isolate the variable r.
1. Start by distributing the -4 to both terms inside the parentheses:
-4r - 4(7) = -79
2. Simplify:
-4r - 28 = -79
3. Move the constant term to the right side of the equation by adding 28 to both sides:
-4r = -79 + 28
-4r = -51
4. To isolate r, divide both sides of the equation by -4:
r = (-51) / (-4)
Now, we can simplify the fraction:
r = 51/4
To check if this answer is correct, substitute the value of r back into the original equation:
-4(r+7) = -79
Replace r with 51/4:
-4(51/4 + 7) = -79
Simplify:
-4(51/4 + 28/4) = -79
-4(79/4) = -79
Multiply:
-316/4 = -79
Simplify the left side:
-79 = -79
The left side is equal to the right side, so the solution is correct.
Therefore, r = 51/4.
To solve the equation -4(r+7) = -79, we can begin by distributing the -4 on the left side of the equation:
-4r - 4(7) = -79
-4r - 28 = -79
Next, we can isolate -4r by adding 28 to both sides of the equation:
-4r = -79 + 28
-4r = -51
To solve for r, we divide both sides of the equation by -4:
r = -51 / -4
Simplifying the expression on the right side gives us:
r = 51/4
Therefore, the solution to the equation -4(r+7) = -79 is r = 51/4.
To check this answer, we can substitute 51/4 for r in the original equation:
-4(51/4 + 7) = -79
Simplifying the expression inside the parentheses:
-4(51/4 + 28/4) = -79
-4(79/4) = -79
Multiplying -4 by 79/4:
-316/4 = -79
Dividing -316 by 4:
-79 = -79
Since both sides of the equation are equal, we can conclude that r = 51/4 is the correct solution.