4+2(5x-8)=ax+b
what values of a and b would make the equation have infinite solutions
a= b=
not again!
expand the left and make the coefficients equal
To have infinite solutions, the equation needs to be always true, regardless of the values of x. This can happen if the coefficients of x on both sides are equal and the constant terms on both sides are also equal.
Let's solve the equation step-by-step:
4 + 2(5x - 8) = ax + b
First, distribute 2 over (5x - 8):
4 + 10x - 16 = ax + b
Combine like terms:
-12 + 10x = ax + b
Next, let's separate the x terms and the constant terms:
10x - ax = b - 12
Factor out x:
x(10 - a) = b - 12
Now, for this equation to have infinite solutions, the coefficient of x on both sides needs to be equal (10 - a = 0) and the constant terms on both sides need to be equal (b - 12 = 0).
Solve for a:
10 - a = 0
a = 10
Solve for b:
b - 12 = 0
b = 12
Therefore, if a = 10 and b = 12, the equation will have infinite solutions.
To determine the values of a and b that would make the equation have infinite solutions, we need to simplify the equation and find the conditions under which it holds true.
First, let's simplify the equation step by step:
4 + 2(5x - 8) = ax + b
Start by applying the distributive property within the parentheses:
4 + 10x - 16 = ax + b
Combine like terms:
10x - 12 = ax + b
Now, let's analyze the equation:
For the equation to have infinite solutions, the coefficients of x on both sides of the equation (10 and a) must be equal, and the constant term (-12 and b) must also be equal.
Therefore, we have two conditions to satisfy:
1. 10 = a
2. -12 = b
Thus, the values of a and b that would make the equation have infinite solutions are:
a = 10
b = -12