3(4x - 2) = 2(6x - 3)
one solution
infinite solutions **
no solution
a+5 = 1/5(5a + 25)
one solution
infinite solutions
no solution **
3(4x - 3) - 7x = 5x - 9
one solution
infinite solutions
no solution
8+2(8x - 6) (choose all that apply)
2(4x + 7)
9x – 10
16x – 4 **
4(4x – 1)
#1 yes
#2:
a+5 = (1/5)(5a+25)
a+5 = a+5 ----> 5=5 , statement is true
infinite number of solutions
#3
3(4x - 3) - 7x = 5x - 9
12x-9-7x=5x-9
5x-9 = 5x-9
true, so infinite number of solutions
#4 yes
To solve the equations step-by-step:
1) 3(4x - 2) = 2(6x - 3)
Expanding both sides:
12x - 6 = 12x - 6
Subtracting 12x from both sides:
-6 = -6
Since the equation simplifies to a true statement (-6 = -6), this means that the equation has infinite solutions.
2) a+5 = 1/5(5a + 25)
Expanding the right side:
a + 5 = a + 5
Subtracting a from both sides:
5 = 5
Since the equation simplifies to a true statement (5 = 5), this means that the equation has infinite solutions.
3) 3(4x - 3) - 7x = 5x - 9
Expanding the left side:
12x - 9 - 7x = 5x - 9
Combining like terms:
5x - 9 = 5x - 9
Subtracting 5x from both sides:
-9 = -9
Since the equation simplifies to a true statement (-9 = -9), this means that the equation has infinite solutions.
4) 8 + 2(8x - 6)
Distributing the 2 to (8x - 6):
8 + 16x - 12
Simplifying:
16x - 4
The equation 8 + 2(8x - 6) simplifies to 16x - 4.
To solve these equations, we can follow the steps below:
1. Distribute the terms on both sides of the equation if necessary.
2. Combine like terms on each side of the equation.
3. Move all variable terms to one side of the equation and all constant terms to the other side.
4. Simplify and solve for the variable.
Let's go through each equation to identify the correct solution:
1. 3(4x - 2) = 2(6x - 3)
Start by distributing the terms:
12x - 6 = 12x - 6
In this case, the equation is consistent and will have infinite solutions. So the correct answer is "infinite solutions."
2. a + 5 = 1/5(5a + 25)
Begin by distributing the terms:
a + 5 = a + 5
This equation is consistent and has the same variable terms on both sides. So the correct answer is "no solution."
3. 3(4x - 3) - 7x = 5x - 9
Distribute the terms:
12x - 9 - 7x = 5x - 9
Combine like terms:
5x - 9 = 5x - 9
This equation is consistent, and the variable terms are the same on both sides. Thus, the correct answer is "infinite solutions."
4. 8 + 2(8x - 6)
Apply the distributive property:
8 + 16x - 12
Combine like terms:
16x - 4
The equation is in terms of the variable only, with no constant term. Therefore, it will have a solution for every value of x. The correct answer is "infinite solutions."