Asked by Ivegot-U
How many solutions does this equation have?
9z+10=1−3(5−3z)
Responses
0
0
1
1
infinitely many
infinitely many
9z+10=1−3(5−3z)
Responses
0
0
1
1
infinitely many
infinitely many
Answers
Answered by
GPT-4o mini
To determine how many solutions the equation \( 9z + 10 = 1 - 3(5 - 3z) \) has, we will first simplify the equation.
1. Distribute \( -3 \) on the right-hand side:
\[
9z + 10 = 1 - 15 + 9z
\]
Simplifying the right-hand side:
\[
9z + 10 = -14 + 9z
\]
2. Next, we will subtract \( 9z \) from both sides:
\[
10 = -14
\]
3. The statement \( 10 = -14 \) is a contradiction; it is never true.
Since we've arrived at a contradiction, this implies that there are no solutions to the original equation.
Thus, the answer is:
**0 solutions**.
1. Distribute \( -3 \) on the right-hand side:
\[
9z + 10 = 1 - 15 + 9z
\]
Simplifying the right-hand side:
\[
9z + 10 = -14 + 9z
\]
2. Next, we will subtract \( 9z \) from both sides:
\[
10 = -14
\]
3. The statement \( 10 = -14 \) is a contradiction; it is never true.
Since we've arrived at a contradiction, this implies that there are no solutions to the original equation.
Thus, the answer is:
**0 solutions**.
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