QuestionSolve for $x$ : $7 x-9=3 x-5$

Studdy Solution

STEP 1

1. The equation $7x - 9 = 3x - 5$ is a linear equation.
2. The goal is to find the value of $x$ that satisfies the equation.
3. Basic algebraic operations such as addition, subtraction, and division will be used.

STEP 2

1. Simplify the equation by moving all terms involving $x$ to one side.
2. Simplify the equation by moving constant terms to the other side.
3. Solve for $x$ by isolating it.
4. Verify the solution by substituting it back into the original equation.

STEP 3

Subtract $3x$ from both sides of the equation to move all terms involving $x$ to one side:
$7x - 3x - 9 = 3x - 3x - 5$
Simplify the equation:
$4x - 9 = -5$

STEP 4

Add 9 to both sides of the equation to move constant terms to the other side:
$4x - 9 + 9 = -5 + 9$
Simplify the equation:
$4x = 4$

STEP 5

Divide both sides by 4 to solve for $x$ :
$\frac{4x}{4} = \frac{4}{4}$
Simplify the equation:
$x = 1$

STEP 6

Verify the solution by substituting $x = 1$ back into the original equation:
Original equation: $7x - 9 = 3x - 5$
Substitute $x = 1$ :
$7(1) - 9 = 3(1) - 5$
Simplify both sides:
$7 - 9 = 3 - 5$
$-2 = -2$
Both sides are equal, verifying that the solution is correct.
The solution is:
$\boxed{1}$

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