Question

problem 8
kadeem is solving the linear equation
$x - 3(2 - 3x) = 2(5x + 3)$.

here are his final two steps.

select the statement that correctly describes kadeems solution
the solution is the ordered pair $(-6, 6)$.
the solution is $x = 0$.
there are infinitely many solutions since $-6 = 6$ is a false statement.
there is no solution because $-6 = 6$ is a false statement.
kadeem
$-6 + 10x = 10x + 6$
$-6 = 6$

Explanation:

1. First, analyze the equation transformation: From \(-6 + 10x = 10x + 6\), we subtract \(10x\) from both sides, getting \(-6=6\).
2. A linear equation of the form \(a = b\) (where \(a

eq b\)) has no solution because there's no value of \(x\) that can make the equation true.

1. Now check the options:

• The first option is wrong because it's a linear equation in one variable, not a system with an ordered pair solution.
• The second option is wrong as substituting \(x = 0\) into \(-6+10x=10x + 6\) gives \(-6=6\), which is false.
• The third option is wrong because a false statement means no solution, not infinitely many.
• The fourth option is correct because \(-6 = 6\) is false, so the equation has no solution.

Answer:

There is no solution because \(-6 = 6\) is a false statement.