Equivalent Expressions Practice
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Question
What value of a would make the expression a(x+3) equivalent to 7x+21 ?(1 point)
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To make the expressions equivalent, we need to distribute the a value into the parentheses. This gives us:
a(x+3) = ax + 3a
Since this expression is equivalent to 7x+21, we can set up the equation:
ax + 3a = 7x + 21
Now, we want to isolate the terms with a on one side of the equation. We can do this by subtracting ax from both sides:
3a = 7x + 21 - ax
Next, let's rearrange the terms to simplify the equation:
3a = 21 + 7x - ax
To further simplify, we can factor out an a from the right side:
3a = (7 - a)x + 21
Now, we can see that the left side of the equation is independent of x, meaning it only contains the variable a. In order for the equation to hold true for all values of x, the coefficient of x on the right side must be zero. Therefore, we have:
7 - a = 0
Solving for a, we find:
a = 7
So, the value of a that would make the expression a(x+3) equivalent to 7x+21 is a = 7.
Question
What value of y would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2?(1 point)
enerate an expression equivalent to: 4(h+2)+2(h+1) . The answer should be in simplest form.(1 point)
h+
its wrong
What value of a would make the expression a(x+3) equivalent to 7x+21 ?
Generate an expression equivalent to: 5+6b+12c+10b−4c−2 . In the simplest form of the equivalent expression, what is the coefficient of variable b ?(1 point)
To simplify the expression 5+6b+12c+10b−4c−2, we need to combine like terms.
Combining the terms with variable b, we have 6b + 10b:
6b + 10b = (6 + 10)b = 16b
The coefficient of variable b in the equivalent expression is 16.
To make the expressions equivalent, we need to combine like terms on both sides. Let's simplify the expression yb−6+7+2b−3b+1:
On the left side, we can combine the like terms with b:
yb + 2b - 3b = (y + 2 - 3)b
And we can also combine the constant terms (-6 + 7 + 1):
-6 + 7 + 1 = 2
So the simplified left side of the equation becomes:
(y + 2 - 3)b = (y - 1)b
Now, we want the simplified left side to be equivalent to 5b + 2. This means:
(y - 1)b = 5b + 2
To solve for y, we need to isolate the terms with y on one side of the equation. We can do this by subtracting 5b from both sides:
(y - 1)b - 5b = 5b + 2 - 5b
Simplifying:
(y - 1 - 5)b = 2
Combining like terms:
(y - 6)b = 2
Now, we want the coefficient of b on the left side to be 1. To achieve this, we can divide both sides of the equation by (y - 6):
b = 2 / (y - 6)
So, the value of y that would make the expression yb−6+7+2b−3b+1 equivalent to 5b+2 is y = 6.
To simplify the expression 4(h+2)+2(h+1), we need to distribute the coefficients to the terms inside the parentheses. This gives us:
4h + 8 + 2h + 2
Now, we can combine like terms:
(4h + 2h) + (8 + 2)
This simplifies to:
6h + 10
So, the expression that is equivalent to 4(h+2)+2(h+1) in its simplest form is 6h + 10.
To make the expressions equivalent, we need to distribute the a value into the parentheses. This gives us:
a(x+3) = ax + 3a
Since this expression is equivalent to 7x+21, we can set up the equation:
ax + 3a = 7x + 21
To solve for a, we need to isolate the terms with a on one side of the equation:
ax - 7x = 21 - 3a
Factor out the a on the left side:
x(a - 7) = 21 - 3a
Now, divide both sides by (a - 7):
x = (21 - 3a)/(a - 7)
So, the expression a(x+3) would be equivalent to 7x+21 if the value of a is (21 - 3a)/(a - 7).