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Math  /  Algebra

Question8. [-/1.61 Points]
DETAILS MY NOTES OSCOLALG1 2.2.904.XP. Solve for the variable. 8(5+1)−23b=b8(5+1)-23 b=b b=b=

Studdy Solution

STEP 1

1. The equation 8(5+1)−23b=b 8(5+1) - 23b = b involves basic algebraic operations.
2. We need to solve for the variable b b .
3. The equation is linear and should have a single solution.

STEP 2

1. Simplify the expression on the left-hand side.
2. Combine like terms involving b b .
3. Isolate the variable b b .
4. Verify the solution by substituting it back into the original equation.

STEP 3

First, simplify the expression inside the parentheses:
8(5+1)=8×6 8(5 + 1) = 8 \times 6
Calculate the multiplication:
8×6=48 8 \times 6 = 48
So the equation becomes:
48−23b=b 48 - 23b = b

STEP 4

Move all terms involving b b to one side of the equation. To do this, add 23b 23b to both sides:
48−23b+23b=b+23b 48 - 23b + 23b = b + 23b
This simplifies to:
48=24b 48 = 24b

STEP 5

Isolate the variable b b by dividing both sides by 24:
4824=24b24 \frac{48}{24} = \frac{24b}{24}
Simplify:
2=b 2 = b

STEP 6

Verify the solution by substituting b=2 b = 2 back into the original equation:
Original equation:
8(5+1)−23b=b 8(5 + 1) - 23b = b
Substitute b=2 b = 2 :
8(6)−23(2)=2 8(6) - 23(2) = 2
Calculate each term:
48−46=2 48 - 46 = 2
This simplifies to:
2=2 2 = 2
Since both sides are equal, the solution is verified.
The solution is:
b=2 b = \boxed{2}

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