What value of y would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2?
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-3b−6+7+2b−3b+1 = -4b+2
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yb−6+7+2b−3b+1 = (y-1)b +2
y-1 = 5
y = 6
To find the value of y that would make the expression yb-6+7+2b-3b+1 equivalent to 5b+2, we need to simplify both sides of the equation and then compare the coefficients of b.
Let's simplify the left side of the equation step-by-step:
yb - 6 + 7 + 2b - 3b + 1
Combine like terms:
(yb + 2b - 3b) + (-6 + 7 + 1)
Simplify further:
(y + 2 - 3)b + (2)
Simplify the coefficients:
(y - 1)b + 2
Now, we can compare the simplified left side (yb - 6 + 7 + 2b - 3b + 1) to the right side (5b + 2):
The simplified left side is (y - 1)b + 2
The right side is 5b + 2
For the two sides to be equal, the coefficients of b on both sides must be equal:
y - 1 = 5
Solve for y:
y = 5 + 1
y = 6
Therefore, the value of y that would make the expression yb-6+7+2b-3b+1 equivalent to 5b+2 is y = 6.
To find the value of y that would make the given expression equivalent to 5b + 2, we need to simplify and simplify both sides of the equation and solve for y. Here's how:
1. Start with the given expression: yb - 6 + 7 + 2b - 3b + 1.
2. Combine like terms for the yb and 2b: yb + 2b - 3b.
3. Simplify the expression: yb - b.
4. Rearrange the expression by reordering the terms: -b + yb.
5. Factor out b using the distributive property: b(-1 + y).
6. Simplify the constants: -1 + y.
Now, we can set the simplified expression equal to 5b + 2:
-1 + y = 5b + 2.
To find the value of y, we can isolate it by moving the constants to one side and the variables to the other side:
y = 5b + 2 + 1.
Simplifying further:
y = 5b + 3.
So, the value of y that would make the given expression equivalent to 5b + 2 is y = 5b + 3.