#### Find the number of solutions to each equation

a. 4(x+1) = 2x + 4 b. 9 - 5x + 2 = 4 - 5x c. 6x + 3 = 6x + 3

algebra 1
no solution
solution to a linear equation in one variable
CCSS.HSA1SE-QJ.8
ninth grade
high-school
Algebra

Anonymous

0

a. 4(x+1) = 2x + 4 b. 9 - 5x + 2 = 4 - 5x c. 6x + 3 = 6x + 3

Sangeetha Pulapaka

1

Step 1: Isolate the given variable in the equation

. 4(x+1) = 2x + 4

4x + 4 - 4 = 2x + 4 - 4 (Subtracting -4 from either side)

\Rightarrow 4 x - 2 x = 0 (Isolate the x variables to the left hand side

\Rightarrow 2x = 0

\Rightarrow x = 0

So, this equation has a solution

Step 2 : Isolate the variable in the given equation

9-5x + 2 = 4 - 5x

-5x + 5x = 4 -2 -9

\Rightarrow 0 = -11

So, this equation has no solution

No solution means when there is no variable left. The variable gets cancelled

Step 3: Recall what are like terms in an equation.

https://www.mathsisfun.com/algebra/like-terms.html

Combine the like terms in

6x + 3 = 6x + 3

6x - 6x = 3 - 3

0 = 0

This means the equation has infinitely many solutions

Skills to know before hand:

What is a variable

https://www.mathsisfun.com/definitions/variable.html