-2 + 3b = 5b - 2(2b + 3) How do you solve for b?

1 answer:

6 0

-2 + 3b = 5b - 2(2b + 3) Distribute the -2 through the parentheses.
-2 + 3b = 5b - 4b - 6 Combine like terms
-2 + 3b = b - 6 Bring all "b's" to one side of the equation
-2 + 3b - b = b - b - 6 Combine like terms
-2 + 2b = -6 Bring the 2 to the right side of the equation
-2 + 2 + 2b = -6 + 2 Combine like terms
2b = -4 Isolate b by dividing both sides by 2
b = -4/2 = -2

Answer b = -2

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Step-by-step explanation:

The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.

<h3>Pythagorean theorem</h3>

The theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...

c² = a² +b²

<h3>application</h3>

For the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.

30² = 7.5 +b²

b² = 900 -56.25 = 843.75

b = √843.75 ≈ 29.0473

The length of each support rod is twice this value, so ...

rod length = 2b = 2(29.0473) = 58.0947

Each support rod is about 58.1 cm long.