Solve for x: 7x - 9 = 3x - 5
Understand the Problem
The question is asking to solve the equation 7x - 9 = 3x - 5 for the variable x. This involves isolating x on one side of the equation.
Answer
The solution is \( x = 1 \).
Answer for screen readers
The solution to the equation is ( x = 1 ).
Steps to Solve
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Isolate the x terms
To get all the terms with ( x ) on one side, subtract ( 3x ) from both sides: $$ 7x - 3x - 9 = -5 $$ -
Combine like terms
Now, simplify the equation: $$ 4x - 9 = -5 $$ -
Add 9 to both sides
To isolate the ( 4x ) term, add 9 to both sides: $$ 4x = -5 + 9 $$ -
Simplify the equation
Calculate the right side: $$ 4x = 4 $$ -
Divide by 4
Finally, divide both sides by 4 to solve for ( x ): $$ x = 1 $$
The solution to the equation is ( x = 1 ).
More Information
This type of equation is a linear equation in one variable. The solution found, ( x = 1 ), indicates that when ( x ) is substituted back into the original equation, both sides will be equal.
Tips
- Forgetting to combine like terms properly can lead to incorrect results. Always ensure to simplify each step fully.
- Mixing up the addition and subtraction signs when rearranging terms can also lead to errors. Keep track of signs carefully.
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