What value of y would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2?(1 point)
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What value of y would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2 ?(1 point)
To find the value of y that would make the expression equivalent to 5b+2, we need to simplify the expression and then equate it to 5b+2.
The given expression is: yb−6+7+2b−3b+1.
Let's simplify it step by step:
1. Group the terms with the variable b and the constant terms separately:
yb + 2b - 3b - 6 + 7 + 1.
2. Combine the like terms:
(1y + 2 - 3) b + (7 - 6 + 1).
Simplifying further:
(-3b + 3) + 2.
3. Combine the terms in the parentheses:
-3b + 3 + 2.
4. Simplify:
-3b + 5.
Now let's set this expression equal to 5b + 2 and solve for y:
-3b + 5 = 5b + 2.
We want to solve for y, so let's isolate y in the equation. Subtract 5b from both sides:
-3b - 5b + 5 = 5b - 5b + 2.
-8b + 5 = 2.
Now, subtract 5 from both sides to continue isolating y:
-8b + 5 - 5 = 2 - 5.
-8b = -3.
Finally, divide both sides by -8 to solve for b:
-8b / -8 = -3 / -8.
b = 3/8.
As we can see, the value of y does not affect the validity of the equation 5b + 2. So, any value of y would work, as long as b is equal to 3/8.
Apologies for the mistake in my previous response. Let's correct it.
We need to simplify the expression yb−6+7+2b−3b+1 and set it equal to 5b+2.
First, let's simplify the expression:
yb−6+7+2b−3b+1 = (y+2+1)b + (7−6)
= (y+3)b + 1
To make this expression equivalent to 5b+2, we can set the coefficients of b on both sides equal:
y + 3 = 5
Now, solve the equation for y:
y = 5 - 3
= 2
Therefore, the value of y that would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2 is y = 2.