Solve for x: 7x - 9 = 3x - 5
Understand the Problem
The question is asking to solve a linear equation for the variable x. The equation provided is 7x - 9 = 3x - 5, and the solution requires isolating x on one side of the equation.
Answer
$$ x = 1 $$
Answer for screen readers
$$ x = 1 $$
Steps to Solve
- Move variable terms to one side
Subtract $3x$ from both sides of the equation to get all the $x$ terms on one side:
$$ 7x - 3x - 9 = -5 $$
- Combine like terms
On the left side, combine the $x$ terms:
$$ 4x - 9 = -5 $$
- Isolate the variable
Add $9$ to both sides of the equation to isolate the $x$ term:
$$ 4x = -5 + 9 $$
- Simplify the equation
Calculate the right side:
$$ 4x = 4 $$
- Solve for x
Divide both sides by $4$ to solve for $x$:
$$ x = \frac{4}{4} $$
- Final answer
Thus,
$$ x = 1 $$
$$ x = 1 $$
More Information
The solution $x = 1$ satisfies the original equation. You can verify by substituting $1$ back into the equation:
$$ 7(1) - 9 = 3(1) - 5 $$
which simplifies to:
$$ 7 - 9 = 3 - 5 $$
and both sides equal $-2$.
Tips
- Forgetting to combine like terms correctly.
- Neglecting to check the solution by substituting back into the original equation.
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