9
x
+
5
=
10
(
×
+
3
)
−
x
Solve for
x
. Be sure to show your work.
State whether the single variable linear equation has a solution, no solution, or infinitely many solutions.
Explain your answer in step 2.
Starting with the left side of the equation:
9x + 5
Now let's simplify the right side:
10(x + 3) - x
Distribute the 10:
10x + 30 - x
Combine like terms:
9x + 30
So now our equation is:
9x + 5 = 9x + 30
We can subtract 9x from both sides to get:
5 = 30
This is a contradiction, which means there is no solution to the equation.
Explanation: If we solve the equation step by step, we end up with a statement that is not true (5=30). This shows that there is no value of x that makes the equation true, so there is no solution.